I've seen two approaches taken to autocompletion in shells and similar environments. As far as I know they don't have names, but I think breadth-first and depth-first accurately describe them.
Breadth-first: The Unix shell standard. Pressing tab adds the largest prefix common to all possible completions.
Depth-first: Used in Windows command prompt, Micro editor, and a few other places. Pressing tab will type out the first complete possibility, even if there are others, and pressing tab more will cycle through possibilities.
There are a couple reasons I prefer breadth-first. With depth-first, I can't get the common prefix. If there are a lot of possibilities before the one I want, I have to press tab several times. And if I actually just want the prefix (for example to create a new file), depth-first probably can't help at all. Whereas if I have breadth-first and I just want to get the first suggestion, I can probably just type the first letter after the common prefix and tab again. In other words, breadth-first is better in depth-first's ideal case than vice versa.
And with depth-first, there's state I can't see. There's a difference between having typed
prefix and having typed
pre and completed it to
prefix - in the former case, tab will cycle me through things starting with
prefix, and in the latter case, through things starting with
pre. My command-line is showing the same thing but it means something different. I trip over this occasionally.
Some environments, like fish, use breadth-first completion but move into depth-first if you continue to press tab after a completion that didn't give you a full possibility. This is obviously better than having only one available, but if I only get one, I definitely prefer breadth-first.