The _donburi_ in _gyūdon_ specifically denotes a _bowl of rice_.
The _meshi_ in _gyūmeshi_ just means _rice_ or even more generically _meal_.
Both describe the same thing:
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"See _gyūmeshi_."
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"A rice meal with onions and fried beef [...]. _Gyūdon._ "
I'm not sure which one is preferred in which situation, but personally I see more _gyūdon_ in daily life (caveat: I don't eat it too often though). There are many specialized kinds of _donburi_, while _meshi_ can be used for almost anything edible and is usually just used in the sense of "meal". It can also specifically denote _rice_ though, as in _yakimeshi_ \- "fried rice", which is more often called _chāhan_ though.