As discussed in Do we need a micro-gravity tag separate from Zero-G?, in many situations these two are effectively the same thing. The tag wiki excerpt for the microgravity tag even reads (boldface added):
For questions about environments with extremely low perceived gravity (colloquially referred to as "zero gravity", usually referring to a free-fall environment in space) and the impact of such environments on creatures and technology.
The tag wiki excerpt for the zero-gravity tag reads:
For questions about zero or low gravity environments
I feel that the two tags should be merged.
For discoverability, it might be beneficial to have a "zero gravity" tag synonym. However, since (absent the term free fall environment) the technically more correct term in almost all cases is microgravity, I suggest that microgravity should be the main tag.
Note that microgravity can apply to Earthbound situations as well; for example, it could be applicable on a question about unrestrained falling elevators.