Here is the Murray (the one I described as 9 splines and is approx. 1-1/4" dia):


Here is the Huffy (the one I described as 12 splines and is approx. 3/4" dia):


As you can see they're both Shimano. I have a Park Tool FR-1 and an FR-5, neither of which work on either of these wheels. Any ideas?? Sorry for not knowing much on this topic, but it's kinda confusing...