This might be naive since I am very new to the field, but I wonder about the difference between sequence identity and coverage in multiple sequence alignment of proteins. I imagine the calculation would be simple, but I couldn't find strict definitions of these two terms and how they are calculated. Can somebody possibly provide an example showing how these two terms are calculated (preferably sequences with gaps and the terms not being 100%)? Many thanks.
In high-throughput sequencing applications, we will often refer to "coverage" as the number of unique sequence reads (queries) that align to the same region in a reference sequence. This alignment problem is a subproblem of the alignment domain referred to as "local" alignment, and coverage makes sense in this context as a measure of how many local alignments of short sequences map onto some location in a much larger sequence.
However, the multiple sequence alignment context that you are referring to is likely a bit different, where you do not have a reference sequence and instead try to find some maximally good alignment of a set of query inputs. This is sometimes called the "global" alignment problem. Here you could plausibly compute the number of other sequences that have aligned residues at the same positions as some focal sequence. That would be a bit like "coverage".
But I agree with commenter David that measurements like similarity are probably more useful in practice- they will certainly be highly correlated with such a "coverage" measure in any reasonable example I can imagine.
Minor update: pairwise identity is a very simple measure that just measures the number of residues in one sequence that are aligned to identical residues in a second sequence. I'm surprised that you can't find anything on this, but here is one highly technical discussion that probably covers a bunch of cases that you don't care about.