GAS (GNU's Syntax) for example uses `mov src,dest`, whereas Intel Syntax uses `mov dest,src`. It still assembles down to the exact same instructions.
The problem with GAS is that it's verbose and almost arcane. It requires a lot of extra notation to indicate what you want to do when it's not entirely necessary. There are a lot of quirks and a number of footguns, too.
Intel syntax, on the other hand, is much more human friendly without sacrificing anything. Definitely start with Intel syntax.
The assembler itself might also have a preprocessor included, which allows you to write macros and stuff to automate tedious things or to DRY up code. Just a matter of checking the docs.
Lastly, ISAs are the actual instructions for a CPU - e.g. x86, AMD64, ARM, etc. Every assembler supports one or more of these of course. The syntax is irrelevant.
Hope that helps a bit. NASM is a great way to start.