You guys left out several AA modes.
Just from memory there's Quincunx, CMAA, CSAA, TrAA, Fragment AA, CFAA
For good reason: most of those just aren't used these days. Quincunx and CSAA are old modified versions of MSAA from Nvidia - the former used a 2x sampling pattern but blended the results from neighboring pixel's samples too; low cost but poor visual result. CSAA included a sampling pattern for the primitive coverage of a sub-pixel and use those results in the blending algorithm. TrAA is another one of Nvidia's old systems, that used MSAA for all non-transparent primitives, and SSAA for transparent ones. Nvidia now recommends that developers use a variant of TAA or DLSS, if there's hardware support.
CFAA is AMD's name for their old MSAA implementation from about a decade ago and, depending on the settings used, involved either a custom sampling pattern that had taps outside of the source pixel, or ran an edge detecting algorithm in a pass. Fragment AA was mentioned above - exclusive to Matrox and no longer in use.
CMAA is the only listed that is (a) reasonably new and (b) sort of still around. It's one from Intel - an evolution of their original
MLAA and subsequent enhancements, such as
SMAA - and it's another post processing edge-detecting algorithm. Visually superior to FXAA and roughly similar in terms of performance (sometimes worse, sometimes better), it's not seen widespread adaptation.