Difference between an Sonata-Allegro Form and a Concerto

This was an interesting question I found on the internet today so I thought I'd take some time to try to answer it without making it too complicated:

The Concerto Form is usually for a solo instrument, accompanied by an orchestra. The work is in 3 movements:

• First movement - Sonata or Sonata-Allegro Form
• Second movement - Ternary Form
• Third movement - Rondo Form or Sonata Form

The above is known more as the Classical Concerto Form and did not begin until the late Baroque era. It was developed from the Concerto Grosso Form in which a small group of instruments or singers act as the "solo" instead of a solo instrument.

The Sonata or Sonata-Allegro Form is usually the form used in the first movement of a work. It could sometimes be used in later movements as well, but essentially, it is a form of a movement versus the form of a work like the Concerto above.

The skeleton of the form is made up of:

• Exposition
• Development
• Recapitulation

It could include an Introduction prior to the Exposition and a coda at the end of the Recapitulation.

Examples of each section:

Exposition:
First Subject - Transition - Second Subject - Codetta

Development:
There could be multiple key changes in the Development section. Like a "middle-child syndrome," this section usually is less stable and has more "quirks" than the other two sections.

Recapitulation:
A variation of the Exposition, this section and consists of the First Subject - Transition - Second Subject.

Coda:
Known as the "tail," this section and brings the movement to an end. It could be short and sweet or very long and elaborate.