No, these two years are very different body styles. The top structure and cover is very differently shaped. you can the convertible top frame been all the same in those years
I have successfully replaced a convertible top on my 95 mustang and published an article on how to do it. See the link below.
You can get a new top for your 1993 Mustang at Mustangs Unlimited.
Behind the back seat
According to the 2003 Ford Mustang Owner Guide : ( Motorcraft MERCON automatic transmission fluid is used for the convertible top )
How do you put the top down on a 1998 Chevrolet Convertible
( # 20 ) is a 15 amp fuse for the covertible top switch on a 2003 Ford Mustang