Bottom bracket tool won't fit

I have the Park tool, but I also have a double sided tool which I acquired so long ago I can't remember where. This tool has the larger splines on one side and the smaller on the other so that's how I know there must have been 2 sizes at one point.

Fair enough, never seen a double sided tool.

I've seen tools like the op posted where the splines are quite short and stubby and then ones like my RaceFace one,

where the splines are much longer but the actual diameter of the splines is the same and (axles aside) both will work on the same bbs.