From a teaching standpoint there are a few important differences between the saxophone and clarinet in terms of embouchure and tone production.
- mouthpiece goes straight into the mouth
- embouchure "EE" muscles pull out "OO" muscles push in, "OO's" win the tug-o-war
- chin is "rounded" slightly
- bottom lip stretched over the bottom teeth just enough to cover
- played (generally) with warm air
The clarinet input pitch with the mouthpiece + barrel should be F# concert or slightly higher (on a short barrel).
- mouthpiece goes down at a 45 degree angle
- embouchure "EE" muscles pull out "OO" muscles push in, tug-o-war ends in a tie
- chin is held flat
- slightly more bottom lip over the teeth to provide a "cushion" for the reed
- played (generally) with fast cold air
So how do you change the type of air than you blow in? (last bullet point).