It is indeed a different song. Taylor wrote it ~1968 and you can find it on the first James Taylor album (along with "Goin to Carolina in My Mind"). That first album was released about a year before the monster Sweet Baby James came out.

You might remember the chorus:

And I feel fine anytime she's around me now
She's around me now just about all the time
And if I'm well you can tell she's been with me now
She's been with me now, quite a long,long time
And I feel fine