What is the difference between sonatas and concertos?

What is the difference between sonatas and concertos?
The two forms are somewhat similar in structure, as they are also similar to symphonies. They have three or four movements (most often, not always) and the first movement is called "sonata form," a theme being developed, a second theme then being developed, and the first theme being reprised (that is an inadequate description and you can find a better one in any textbook).
As to your question, a sonata is played by one instrument (e.g. piano) or one instrument accompanied by piano (e.g. violin, cello, indeed any instrument at all). A concerto is played by one instrument (usually) with a symphony orchestra. (There is a Brahms double concerto for violin and cello, and a Beethoven triple concerto for violin, cello and piano.)