Ich weiß nicht, ob es einen Unterschied zwischen etwa und ungefähr gibt und wann man welches Wort benutzt.
Etwa und ungefähr are both adverbs. You can use them interchangeably in the sense of approximately.
Ungefähr, however, is also an adjective. You can't replace this adjective with etwa. (But you can still reword the sentence using the adverb and then, again, use both words interchangeably.)
The corresponding adjective to etwa would be etwaig, which has a different meaning: possibility.
There are also use cases of etwa in which you must not replace it with ungefähr; namely, when giving an example.
1 eventuell not equals eventual
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It's the same, you can use whichever you want.
Both are used often, so it doesn't matter which you choose.