Both 遇到 and 碰到 can be translated to "come across/run into" in those sentences:
遇到大学同学了。
碰到大学同学了。
What's the difference between 遇到 and 碰到?
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"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 like to think of 碰到 as the equivalent of the English "bumped into"
And 遇到 as the English "came across" or "encountered".
The later being more formal and first being more oral in both the English and Chinese.
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.