Like I said
another two (or)
there are two more (or)
two other people were arrested
Do they have different meanings or implications?
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There is a difference. "Another" is ambiguous. It can mean "different" or "additional". By contrast, "more" (as in "two more people were arrested") can mean "additional" but cannot mean "different". So if you mean "additional", it would be better to use "more", because "more" avoids that ambiguity.
The leading "There are" isn't required, and essentially no difference exists between the following sentences:
Two more people were arrested.
Two other people were arrested.
Another two people were arrested.
Since only humans can be arrested, the same meaning can be conveyed even more briefly as follows:
Two more were arrested.
Two others were arrested.
Another two were arrested.
Note that "other people" changes to "others" in the second example (because "other" as a pronoun is countable, unlike "more").