Tchad Blake/Bonnie Raitt 'Fundamental' snare sound

I was wondering if anyone would know what it is about the snare sound in songs like Spit Of Love and The Fundamental Things. You can't hear the spring of the snare and the snare is so snapy kind of warm sound. I don't how to describe it. I love the sound.

Would anyone know what it is? Is it the snare itself, the skins, or dampening ( resonant head perhaps) that mainly contributes to that sound?

Thanks

Tchad Blake/Bonnie Raitt 'Fundamental' snare sound