Motives versus Motifs

Dear Donu, here are Grothendieck's own words:

"Contrary to what occurs in ordinary topology, one finds oneself confronting a disconcerting abundance of different cohomological theories. One has the distinct impression (but in a sense that remains vague) that each of these theories “amount to the same thing”, that they “give the same results”. In order to express this intuition, of the kinship of these different cohomological theories, I formulated the notion of “motive” associated to an algebraic variety. By this term, I want to suggest that it is the “common motive” (or “common reason”) behind this multitude of cohomological invariants attached to an algebraic variety, or indeed, behind all cohomological invariants that are a priori possible"

They can be found in his autobiographical "Récoltes et Semailles", where there is also an allusion to a musical meaning of "motif".

The translation is Barry Mazur's in his article "What is... a Motive?" which is, needless to say, a fascinating short survey (plus bibliography) .Here is the reference:

http://www.ams.org/notices/200410/what-is.pdf

Motif in french has both the meaning of english "motive" and of "pattern". It is still actively used in decorative arts and art history "Cette tasse est ornée d'un très joli motif", "This cup is decorated with a very pretty pattern", and so on for tapestry, greek freeze, wallpaper, etc. And still used when describing a police case : "Il a un alibi et n'a aucun motif".

So I believe that Grothendieck was well aware of this ambiguity.