The key difference is that Arc Hydro fill allows you to specify "deranged" polygons as input. These areas will NOT be filled. So it is a different option than standard fill that can limit the fill by depth. Document that Dan pointed you to goes into details on how to identify and manage sinks if you choose to have them. Note that if you are going to do full terrain preprocessing (so you can use AH tools for watershed delineation etc.), you need to tweak the flow direction in sinks (described in that document as well).
And finally, if you are using Pro 3.0 and up, there are tools that allow you to do flow direction and accumulation without filling sinks. In general, it provides better results than using the fill approach.