What is the difference between rhyme and rhythm?

Answer 1

Rhyme -- sounds (and usually spellings) that are the same:

hop
bop

rain
plain

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Rhythm -- arrangement of stressed and unstressed syllables in a line of poetry that creates a pattern (and often a "beat")

The RAIN in SPAIN falls MAINly in the PLAIN

Answer 2

http://en.wikipedia.org/wiki/Rhyme

and

http://en.wikipedia.org/wiki/Meter_(poetry)