confused about logins to .org and .com

I’m confused about logging in to wordpress. I’m told I need to access my account at wordpress.com in order to find my API, to be able to use a plugin. But my logon doesn’t seem to work at the .com site. It works at wordpress.org, but that doesn’t seem to have a ‘my account’ button, unless I’m missing it. Are the two sites separate/different things, then?
I’ve tried creating a new account at .com, but get told the user name already exists, which suggests it recognizes my user name (unless someone else has the same one there). But the password that works at .org doesn’t work there (I’ve reset the .org one a couple of times while trying all this). And if I request a new password in the .com login section, it doesn’t come to my email address.
Bottom line is, I can’t seem to access the API, so can’t use the plugin.
None of this affects me logging in to my site itself (which has a different username, via the web host).
Any help appreciated.