He will pay us a short visit.
is equivalent to
He will pay us a brief visit.
However, the adverbs briefly and shortly have a rather different meaning. The sentence
He will come over briefly.
means that he will come over and stay for a short time, whereas the sentence
He will come over shortly.
implies that he will come over very soon and stay for an unspecified amount of time.
As you can see, using the wrong word can completely change the meaning. Depending on the context, that may have dramatic consequences. The warning:
We will briefly switch off the internet.
sounds rather harmless, whereas
We will shortly switch off the internet
will make people much more nervous!