First of all, it's "come across someone," not "come across TO someone."
"Run into someone" means the same thing as "come across someone," which means to accidentally see someone you know. For example, you can run into your friend on the street, or you can come across your friend on the street. "Come across" has a broader meaning in that it doesn't just apply to people. For example, you can come across some money, or come across a new word.
To "meet someone" has several meanings. One is to get to know someone you didn't know before. I'm sure everyone's heard of "nice to meet you." The second is to make plans to see someone at a particular time and place. For example, I'm meeting my friend at the train station. The third is the same as to "run into someone" and "come across someone." For example, I met him on the street the other day.