Here's what Webster's 1913 edition dictionary says:
Fantasia: \Fan*ta"si*a\, n. [It. See {Fancy}.] (Mus.)
A continuous composition, not divided into what are called
movements, or governed by the ordinary rules of musical
design, but in which the author's fancy roves unrestricted by
set form.
Rhapsody \Rhap"so*dy\, n.; pl. Rhapsodies. [F. rhapsodie, L.
rhapsodia, Gr. "rapsw,di`a, fr. "rapsw,do`s a rhapsodist;
"ra`ptein to sew, stitch together, unite + 'w,dh` a song. See
Ode.]
1. A recitation or song of a rhapsodist; a portion of an epic
poem adapted for recitation, or usually recited, at one
time; hence, a division of the Iliad or the Odyssey; --
called also a book.
2. A disconnected series of sentences or statements composed
under excitement, and without dependence or natural
connection; rambling composition. ``A rhapsody of words.''
--Shak. ``A rhapsody of tales.'' --Locke.
3. (Mus.) A composition irregular in form, like an
improvisation; as, Liszt's ``Hungarian Rhapsodies.''
Now doesn't that just clear things up?
