Yes, R square should be the square of the correlation coefficient. The correlation coefficient is often called R so R square is R^2.

The reason they aren't matching could be due to a few reasons.

1. You've miscalculated something

2. People use different definitions of the standard deviation. Often the "sample" standard deviation uses /(n-1) instead of /n to inflate the deviation slightly to adjust for the fact that you only have a sample. So if your calculations use different standard deviation methods, they won't match.

3. If R^2 is being defined as 1 - SSE/SST, then it might not match.

In short, they do measure the same thing. So you really could just pick one. If you want to go deeper in to it, you can post a sample and the two values your getting, and I'll help you sort out why. If you are fine just knowing that someone with a Math degree says you're right and you can use the correlation coeffitient to get R^2, then that's good too.