Clarinets have a wooden body (less expensive models can be made of plastic or even metal) and use a single reed attached to a mouthpiece. The Soprano and Bass Clarinets are separated by an octave. On Soprano Clarinet Eddie Daniels is one of my favorite jazz clarinetists currently recording and touring. Eric Dolphy (another personal favorite) recorded with John Coltrane and others on Bass Clarinet. Benny Goodman, Artie Shaw, Buddy DeFranco are all important players from the swing era (1940's thru 1950's).
In the picture to the right, the Bass Clarinet is on the left, and the Soprano Clarinet is on the right.