I took the TEF. There are places that also have the TEF-AQ, which is explicitly for those immigration to Quebec. It's shorter than the original TEF, only Oral Expresion and Listening, but the downfall is that results go directly to immigration, so if you do poorly you don't have the choice to not send it in.
The full TEF is Listening, Grammar, and Reading Comprehension. In addition, for Quebec purposes you have to do an extra TEF portion for Oral Expression. It's not a bad test, and I did pretty well on it, but the problem is it's exhausting. Mine was 3.5 hours long, and I feel I would've done better if I hadn't been so tired (the oral part was the last part, which made it even harder). The TEF is also a general test - it's for all levels, and your grade will indicate your level.
I believe the TCF is pretty similar, not sure.
The DELF, on the other hand, is divided by levels. So if you have little knowledge of French, you take the DELF A1, and if you pass it, you have an A1 level. So you take different tests depending on the level you think you have, and you try to pass it. I haven't taken it though, so I can't speak much about it.