The Structure of the Clarinet
The clarinet-unique among wind instruments?

A two-clarinet set-the relationship between the A clarinet and B♭ clarinet

Although the A clarinet is 1 cm longer, the two clarinets do not look much different from one another. However, the instruments produce different notes-A is the root note of the scale for the A clarinet, while B♭ is the root note of the scale for the B♭ clarinet.

What is the difference between the A clarinet and the B♭ clarinet?

Musical score for the clarinet

For example, when a musical score for the clarinet reading C, D, E, F, G, A, B, C is played on an A clarinet, the actual notes played will be A, B, C♯, D, E, F♯, G♯, A, while if the same score is played on a B♭ clarinet, the actual notes played will be B♭, C, D, E♭, F, G, A, B♭. Let's listen to the notes.

Musical score for the clarinet

Actual notes played on an A clarinet

Actual notes played on an A clarinet

Actual notes played on an B clarinet

Actual notes played on an B clarinet

The pitch of the two instruments differs by a semitone.
There is also an inherent difference in timbre between the A clarinet and the B♭ clarinet. Since the A clarinet possesses a deep, sonorous sound, it is used for quiet pieces, and since the B♭ clarinet has a bright sound, it is used for dances and stirring pieces. The composer specifies which clarinet is to be used.
The musical score reveals that the A clarinet plays three sharp notes. Playing pieces in the key of A major using an A clarinet is straightforward, as the instrument's basic scale is A, with these three sharp notes, and it is also easy to play pieces in D major (which has two sharp notes) and E major (which has four sharp notes) on the instrument, as these include only a single flat note or single sharp note on the clarinet score. Conversely, since the B♭ clarinet starts out with two flat notes already, it is good for playing pieces that include several flat notes, as indicated by the 'b' on the left hand side of the score.

In short, the A clarinet is intended for pieces with sharp notes, while the B♭ clarinet is intended for pieces with flat notes. Although it is a little hard to imagine, as a result of this clarinetists take to the stage with both an A clarinet and a B♭ clarinet, and switch between them to suit the different pieces they play.

Why switch between the two?

For example, the clarinetist may switch instruments between the first and second movements of a work, if they are in different keys, or may even switch during a piece if there is a change of key. The clarinetist will swiftly transfer the mouthpiece and the reed to the other instrument and start playing it. Alternatively, the clarinetist may switch the barrel from one instrument to the other. The clarinet is a busy instrument.