They're not synonym, they have the same description.
What's the difference? Should we make them as synonym tag (one of them) or what?
I agree that on most existing questions here they are used for the same thing and should be merged, but I think the word "maintenance" is a bit too potentially ambiguous. instrument-maintenance would make sense, but maintenance as applied to music on the whole (the topic of this site) could have other meanings.
instrument-care by contrast is completely unambiguous, and if we turn maintenance into a synonym for instrument-care it will autocomplete for askers, so if they meant something different by "maintenance" they can choose something else.
I disagree. Some of the first few questions in instrument-care are about how to store a instrument well, which sounds very much like instrument care, but not maintenance.
Yes, there is some overlap, but I think they are subtly different.
I did not look at the questions bearing the respective tags, but the answers above did not much to clarify the definitions. The most important difference for me seems to be: