I run Linux, and have no reason to think other major Unix variants would be much different in this respect, it being mostly a matter of the shell. It is, indeed, just as simple in Linux as you describe in DOS; in point of fact, it's exactly the same command. ^_^ "ls > list.txt" will produce a list of all files/directories in the current directory, filenames only; if you want more information, you need other options to ls, but for this purpose the filenames are enough.
Which was probably more information than you wanted...
Which was probably more information than you wanted...