Ottava rima vs. rhyme royal vs. terza rima

Here is a relevant quote from the 1990 spring issue of Poetry Review: Poetic comedy needs strong form, needs a momentum sufficient to get the form bedded in the reader's subconscious, the heroic couplet of the Augustans, the ottava rima of Byron and Auden.
Ottava rima is a form of poetry consisting of stanzas of eight lines of ten or eleven syllables rhyming abababcc.
Rhyme royal is that form of verse which consists of stanzas of seven ten-syllable lines, riming a b a b b c c.

Terza riman is an Italian form of iambic verse, consisting of sets of three lines, the middle line of each set riming with the first and last of the succeeding (a b a, b c b, c d c, etc.).
Definitions were taken from the Oxford English Dictionary.