How to Return Differences between Two Columns?

Hello,

What I'm trying to do is to return differences between two IDs. In the file, column A contains new IDs, and column B contains names associated with it. There's also a column with Old IDs.
I need:
1. to pull IDs from column A that aren't in an old column (pull the differences)
2. to pull list of names from column B that will correspond to the IDs from column A

I hope someone can help here. I tried different formulas, and conditional formatting, but for some reason it doesn't pull all the different IDs.

Thanks.