TXAA/MSAA/SMAA/FXAA/MLAA modes are post-process fiters that have to roughly figure out where edges are with various edge detection algorithms. Because of that, they are significantly cheaper, but less accurate and may soften image if they misdetect edges location and filter a non edge "surface". Or they simply use very primitive technique which almost has no performance hit, but makes image blurry as whole (FXAA for example).
You are bunching all these techniques together, but in fact TXAA/MSAA are much different than SMAA/FXAA/MLAA ... and they all use some form of edge detection (to be as cheap as possible) only super sampling schemes don't, and now I want to write a wall of text.
SSAA is super sampling algorithm, everything is rendered in higher res and then down sampled using reconstruction filter ... DSR is very similar but only in effect - it doesn't scale with powers of two like SSAA, its scaling factor is float so it has to use gauss filter when downsampling instead.
MSAA is a multi sampling algorithm (trying to produce effects of supersampling from the other end), everything is rendered at same res and only pixels that are near the edges of the geometry (because optimization) get multiply sampled (pixel + number of surrounding pixels in a pattern) as subpixels from imaginary supersized image that was never actually rendered. Algorithm is complex, eats VRAM because you gotta save all those subpixels per each pixel, because you wanna handle overdraw correctly (rendering pixel on pixel) and know which subpixel from which original pixel to take into account based on z buffer. Nevertheless, this still misses all aliasing on semi-transparent textured polygons (for example tree leaves and flags with torn edges which both use alpha channel and are done in texture space).
This was fixed in DX9 era in forward rendering engines with Transparency MSAA which is the same algorithm running beside regular MSAA but done whenever sampling each transparent texture in any shader (also only on pixels close to transparent-nontransparent transition in texture space - hence "alpha to coverage" name). We also have a super sampling variant of transparency anti aliasing, everything is the same only SSAA is used when sampling each transparent texture in any shader. Sparse grid variants use different patterns for reconstruction filter that try to have same effect with less samples.
Trouble is MSAA only works properly out-of-the-box on forward rendering technique. Massively more popular and more optimal deferred rendering compose each frame through layers (like in photoshop) and each layer is rendered by shader in screen space (still doing geometry part of the pipeline once) and because that transparency is done differently. To use hardware accelerated MSAA in deferred renderer is tricky (MSAA is too much embedded in the rasterization pipeline - it changes how ROPs work and can't be switched on/off whenever during the frame), and to be careful not to use it unnecessary number of times for same pixel is PITA for devs ... you can technically do it, DX10 and higher allows it with programmable pipeline, but nobody does it except rockstar and crytek.
TXAA is actually regular MSAA plus temporal AA done in screen space in post processing pass. Trouble is devs a) don't know how to "tame" the performance hit of msaa in deferred engines b) can't be bothered to tweak some parameters in temporal post process part (overdriven gauss filter has to be somewhere in there).
SMAA is done in screen space in post processing pass and it's really smaa...art because it's sub-pixel morphological aa ... it has pre-programmed mapping how to resolve different types of features (tiny blocks of several pixels) ... so the subpixel msaa-like logic is pre-calculated through feature mapping stored directly in the shader code. Brilliantly. I also don't understand why it isn't used more. Crysis 3 has it. Probably Star Citizen also because of the crytek engine.
SMAA T1 and T2 are temporal variants, much heavier but without shimmering when still, however with ghosting when moving.
FXAA is fast and approximate also done in screen space in post processing pass.
MLAA is also aproximate also prost processing but with temporal aa which doesn't handle well shimmering when still and ghosting when moving.