Recorders exist in different sizes. Most of them are transposing. Also they exist in C and in F. This is just a selection, and doesn't show all recorders that are used today.

All modern clarinets. The third from the left is in C, and non transposing. All the others are transposing instruments.

A Trumpet. The most common Trumpets are in B flat; they sound two semitones lower than they are notated, and are tramsposing instruments. As with many conert instruments, there are many different kinds of trumpet, and some are not transposing.

A transposing instrument is a musical instrument that does not play the notes you might think it will play. But all the notes differ from the real notes by the same musical interval. So a song played on the transposing instrument will sound familiar, but played in a different key. That is because the transposing instrument is tuned above or below what the usual notes would be, and always above or below by the same number of notes on a scale. The usual notes are called "concert pitch". Most non-transposing instruments, like pianos, are tuned to play in the key of C.