Both 遇到 and 碰到 can be translated to "come across/run into" in those sentences:
What's the difference between 遇到 and 碰到?
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Generally the same.
"碰" is more informal than "遇" when used followed by "到" or "见" to form "碰/遇到" and "碰/遇见"
Another difference is that "碰" is more 'physical' as a verb than "遇", E.g.
"碰" is literally "touch", also with meaning "collide" as in "碰撞".
"遇" is more similar to "meet" as in "遇见" or "being through" as in "境遇".
I got the impression that 碰到 implies a more unexpected or accidental meeting than 遇到. I can't find any references to back that up, though. They both seem to imply some element of chance or unpredictability.
In this case, they have the same meaning！