There is only one way to describe the current classification of the protists; a mess. Not so many years the term Protista was used to encompass a variety of single or simple multicelluar eukaryotes and was itself broadly divided into the Protozoa and Algae. The algae were the photosynthetic component of the protists and the protozoa were those which weren't photosynthetic. There were problems with this division, e.g. some otherwise similar organisms had both photosynthetic and non-photosynthetic species.
The traditional classification is still followed by many of the sites you will encounter as you go through the web.
MASTIGOPHORA (FLAGELLATA): These eukaryotes were defined by the presence of a flagellum, a long, thin, thread-like organelle used in propelling the cell through the water. There may be one flagellum or two flagella. The flagellates could be either photosynthetic or non-photosynthetic.
SARCODINA: The Sarcodina included the amoebas and they move by a flowing of the cellular protoplasm by extensions of the cell called pseudopods. The group should lack flagella, although some species of the Sarcodina move by both pseudopods and a flagellum. The Sarcodina were also constituted to include several amoeba like groups with outer shells (tests) composed of either silica (Radiolaria) or calcium carbonate (Foraminifera).
SPOROZOA (APICOMPLEXA). The Sporozoa were comprised of a number of parasitic protozoans and were generally characterized by a lack of characters.
CILIATA (CILIOPHORA). The ciliates were protozoans covered with small hairs. The hairs, moving in waves, propel the organism through the water. The ciliates were also characterized by multiple nuclei; a large or macronucleus, and number of smaller, or micronuclei. The typical example of a ciliate is the famous Paramecium.
PYRROPHYTA. The Pyrrophyta included the dinoflagellates. The dinoflagellates are single-celled organisms, commonly with a complex, highly sculptured outer test composed of cellulose, and possessing two flagella. The dinoflagellates, although photosynthetic, had many of the characteristics assigned to the Protozoa and thus proved very much of an embarassment to the traditional classification.
CHRYSOPHYTA. The Chrysophyta included the diatoms, yellow-green algae, and golden-brown algae in the old scheme of things. The diatoms are the most abundant of this group and are characterized by a double cell wall structure impregnated with silicon, much like an animal enclosed in a petri dish.
PHAEOPHYTA. The brown algae are most commonly multicellular plant-like organisms, some of them very large such as kelp. The group is characterized by the particular form of its photosynthetic chemicals.
RHODOPHYTA. The red algae are marine and characterized by the presence of the red pigment phycoerythrin.
CHLOROPHYTA. The green algae. The green algae were single or multicellular organisms, both marine and freshwater. The group, as defined, is very diverse and is now known to be heterogeneous. It was defined by the presence of the same photosynthetic chemicals found in the plants.
The traditional classification was a functional classification in the sense that it classified organisms on the basis of its possession of one or two characters such as flagella, a particular type of chlorophyll, or outer shell. It made the classification of the "protists" easy and convenient. However the resulting classification did not accurately reflect the evolutionary history (phylogeny) of the species. There are two primary reasons for this failing in the traditional classification.
The Protists do not really exist. The "protists" in reality represent all of the groups of the Eucaryotes after the fungi, animals, and plants have been removed. Our appreciation of nature is dominated by these three groups because they are easily visible and easy to appreciate. Although there are hundreds of organizations devoted to the conservation of birds, plants, reptiles, butterflies, and mammals, there is no "Save the Paramecium Society". However the plants, fungi, and animals represent just three evolutionary lines in the profusion and confusion of eucaryotic groups. All of these other groups became the "Protista".
The various groups of the "protists" were commonly defined by the presence or absence of characters which were not reflective of their evolutionary history. The two most illustrative example are flagella and photosynthesis. Both characters also occur in the Procaryotes (such as bacteria and blue-green algae) and, therefore, cannot define groups in the Eucaryotes. For example if blue-green algae (procaryotes) and algae (eucaryotes) both have photosynthesis, it is impossible to define the "algae" solely on the presence of photosynthesis. One of the basic tenents of systematics is that a group of evolutionarily related organisms can only be defined by the shared possession of a unique derived character. As an example if we define a group of organisms B by their possession of structure A, then structure A must be unique to that group B.
Some years ago the principles of modern systematics and the advent of new techniques such as molecular systematics and the electron microscope were brought to bear on the problem of producing an accurate evolutionary history for the "protists". The result was a complete over-turning of the traditional classification. Some movement toward a new classification has occurred, but as in most revolutions the situation is still extremely unsettled and many of the pieces lay still unresolved on the slaughter house floor. The old characters such as flagella, pseudopods, or photosynthesis no longer work to identify major groups and as you go through the web sites, you will find confusion because of a conflict between the old and new systems and because many of the most familiar "protozoans" are no longer classified into particular groups.
We have tried to come up with a compromise between the old and the new, but are well aware of its weaknesses. One of the more commonly accepted views of the evolutionary history of the Eucaryotes is given in the figure below.
PRIMITIVE GROUPS. This is a group of unplaced "protozoa" like organisms and includes parts of what were considered to belong to the Sarcodina, Sporozoa, and Flagellata in the traditional classification. In essence this group is what is left over after the recognizable groups have been accounted for.
SLIME MOLDS. The slime molds were considered to be part of the fungi in the traditional classification, but are now treated as a separate major lineage of the eucaryotes unrelated to the fungi.
RHODOPHYTA. The red algae are now considered to be a separate lineage of the eucaryotes and unrelated to the other algal groups.
The Foraminifera, Dinoflagellates, ciliates, and Apicomplexa (Sporozoa) are currently considered to represent a single major branch of the eucaryote tree. Although the first three groups are largely unchanged, the Apicomplexa have been restricted to a single group from the old Sporozoa.
RADIOLARIA. Unchanged, but considered to be related to the Chromista.
CHROMISTA (STRAMENOPILES). The Chromista comprise all of the old "algae" except for the Rhodophyta and the "Green Algae".
"GREEN ALGAE". The "green algae" are the "CHLOROPHYTA" of the traditional classification. Presently they are given no particular name because the various groups do not seem to form a completely natural group and their relationship with the plants has yet to be resolved. Just as the fungi, animals, and plants and just three branches of the eucaryote line, the plants are a single line from among many equal lines of "green algae" and no stable classification of the green algae and plants has yet arisen.
CHOANOFLAGELLATA. The choanoflagellates are a group of single celled or colonial flagellates that are believed to be most closely related to both the fungi and the animals.
FUNGI. The fungi are now believed to be more closely related to animals than they are to plants.
If you are confused, so are we. Much remains to be resolved, so do not be dissapointed if your travels through the web leave you a bit confused. Everyone else is as well.