Log in to .com and .org at the same time?

Hi.
I’m new to WordPress and facing the .com/.org queries. I run a self-hosted blog via .org, but needed an API key to check stats, so I registered another account at .com .

I have my API key and installed the stats plugin on the .org self hosted blog. Rather than blow it, I use two different browsers to look at the different accounts: Safari for .org, Firefox for .com . Can I use one browser to login to the different accounts, since they are different domains? Or will that jam me up, since I’m using the API key in both?

Finally, I hope what I’m doing is what I want to achieve. The goal, simply, is to get my stats

Please advise. I’m grateful, in advance.
Scott