Interestingly the flagellar structures seem to be fairly conserved in evolution, and are often used in taxonomy. Most eukaryotes are fundamentally biflagellate, meaning their flagellar systems, whatever they are, are likely derived from modifications of an ancestral biflagellate form, and retaining the double basal bodies. Flagella can be lost, but the basal bodies that anchor them tend to remain behind. Conversely, basal bodies can be duplicated, as they have, for example, in parabasalia, which are tetraflagellate; entire basal body units (kinetids) can also be multiplied, up to extremes such as in ciliates. (the developmental organisation of ciliate flagella is an endlessly fascinating subject, and if all goes well, would be my research focus after BSc. =D *knocks on
In contrast, a few eukaryotes have what is fundamentally a single flagellum - those are unikonts, which include amoebozoa (eg. cellular slime moulds) and opisthokonts (ass-tails, eg. fungi, choanoflagellates...and us). It is intuitive to think of flagella as propelling the organism forward. But not everything is about sperm: most eukaryotic organisms actually pull themselves by flagellar motion, thereby defining the location of the flagellum as the anterior end, rather than posterior. Another distinction is between isokonts (equal flagella) and heterokonts (unequal flagella) - in the former, the two flagella are structurally identical, whereas in the latter they differ, often with little protrusions (mastigonemes) lining one of them.
Actually, scratch everything I just said about opisthokonts and amoebozoa being unikonts together. Missed a memo... there's this amitochondriate amoeba Breviata (TCoO post here and picture here), previously of uncertain placement or classified as an archamoeba. Despite having a single flagellum, it seems to have a double basal body, one of them unflagellated (Walker et al. 2006 JEM). Turns out that evidence suggests it's a basal amoebozoan, which would kill TC-S' unikont/bikont division (indicated in grey below):
(Roger & Simpson 2009 Curr Biol; numbers indicate ancestral number of basal bodies/flagellar unit, asterisk indicates one basal body is unflagellated, and the 2+ in Breviata indicates there may have been more that two basal bodies/unit.)
So to summarise:
kinetid - unit of basal bodies + flagella; not all basal bodies must have a flagellum (but the flagella must be anchored to a basal body each)
opisthokont - organisms with posterior flagellation; most eukaryotes have flagella at the front of their movement.
heterokont - both (or more) flagella structurally different
isokont - both (or more) flagella are the same
unikont - organisms with single basal body/flagellum per kinetid
bikont - organisms with double (or more) basal body per kinetid
mastigonemes - little protrusions regularly lining a flagellum; for increasing a flagellum's surface area.
centriole/basal body - generally interchangeable
cilium/flagellum - generally interchangeable
(kont means tail, by the way)
I noticed I throw those terms a lot in other posts without really explaining them; so hopefully this post can be some sort of reference, just in case!
There's more to it, but someone has some protist-oriented microscopy for me to do. I love Saturday nights!
Roger, A., & Simpson, A. (2009). Evolution: Revisiting the Root of the Eukaryote Tree Current Biology, 19 (4) DOI: 10.1016/j.cub.2008.12.032
WALKER, G., DACKS, J., & MARTIN EMBLEY, T. (2006). Ultrastructural Description of Breviata anathema, N. Gen., N. Sp., the Organism Previously Studied as "Mastigamoeba invertens" The Journal of Eukaryotic Microbiology, 53 (2), 65-78 DOI: 10.1111/j.1550-7408.2005.00087.x