They look a little different, their properties are a little different and they do different stuff:
A field (except for some fields that only serve layout purposes like info, gap, line) saves something in the content file. A section does not.
A pages field and also a files field are basically SELECT/MULTISELECT fields, i.e. you select something out of a pool of options, which is then stored in the content file.
So, to oversimplify a bit:
fields => content
sections => organization/displaying stuff and additionally uploading/creating files/pages, deleting, sorting, publishing