In my mind, it seems more likely that the signature on the Crown card is the correct autograph, since it seems unlikely that someone else would sign a card with a picture on it. (I know there are shady dealers/collectors out there, but I got this from a reliable source, albeit one that might not have known what a real/fake autograph of Tom's looked like, as I don't either.)
I suppose that anyone can sign an index card, so it's possible that it was signed by another person with the same name, but a quick online search didn't produce any other semi-famous people by the name of Thomas G Fisher. And while there was another baseball player named Tom Fisher who played for the 1904 Boston Beaneaters, his middle name began with a C, so I doubt that this is his autograph.
While I'm sure that whoever sold me both of these autographs had good intentions, they certainly appear to be from two different Tom Fisher's. Since Tom's autograph is rare and I wasn't able to find any other examples online, I'm hoping that one of you might be able to swoop in for the assist. Help a brotha out!