OK, sorry hoops.
Perhaps I was not clear, not the appearance, but the sonic difference, how they influence the sound of the drum?
Thanks
Depends on the drum, & also the structure of the hoops. For example, there's a very big difference between thick ply hoops (that are effectively sonically dead), & segmented or steam bent single ply wood hoops.
Ignoring segmented & steam bent single ply hoops for the moment (simply on the basis that they're more specialised), the
very basic differences as follows;
Triple flange: Typically the lightest of the metal hoop varieties, in this comparison, they add minimal mass to the drum closest to the head. They're pressed, as such, they ring if you strike them. Put these two features together, & these hoops will afford the greatest head sustain, plus add a degree of ring/brightness to the drum's sound. Cross stick sound is usually bright but somewhat subdued compared to die cast.
Die cast: Heavier construction compared to triple flange, but also sonically dead by comparison. (pick up a triple flange hoop, & a die cast hoop, & strike them. The die cast hoop is pretty dead, the triple flange will ring). More mass = grater dampening of the head sustain, & this equates to a drier sound. The greater mass added to the drum will also serve to focus the drum's sound more. Cross stick sound is generally enhanced, & rimshots much louder than with triple flange hoops.
Heavy ply wood hoops: Usually quite heavy, & also sonically dead. They add mass to the drum, plus dampen both head sustain & shell response. They render a metal drum "mellow", and are good for controlling high overtones in both metal & wood drums. Muted cross stick & rimshot sound compared to metal hoops. You'd expect them to make a drum sound more "woody", but they generally don't. That said, they do have their place in a controlling function.
The above summary is extremely basic, & subject to multiple caveats.
Hope that helps, Andy.