Many have adapted to the style of italics instead of underlining, but some have not.
Though few, there are some style guides and manuals that will still insist on underlining and they teach that this is correct.
There have been some “rules” created about these formatting choices.
These rules are generally followed by all writers, regardless of what is being written.
You want to be able to differentiate between the smaller pieces and the title of the collection itself.
This also applies to other forms of publications and media: Rules always have exceptions, and the proper use of italics is no different.
Going back a few generations, writers would make certain words or phrases stand out by simply underlining them.
This would bring extra attention to the words and tell a reader that they were important in some way.
This is an age-old question that has plagued writers and students for years.
There was a time where standards for this didn’t exist at all, and this was due to the overall lack of formatting options in general.