From the definitions of the two, it seems like canto might be a more light-hearted, jovial singing, whereas cano might be more, for lack of a better word, "proper" singing?
According to Döderlein's Hand-book of Latin Synonymes (also here), canere is the more general term for music (and thus may be used for singing), whereas cantare usually is used more specifically to refer to vocal music:
Canere (from καναχεῖν) means, in the most general sense, to make music, voce, tibiis, fidibus, like μέλπειν; cantare, with vocal music, like ἀείδειν;
(Note: Döderlein's assertion that canere is from καναχεῖν is incorrect. According to da Vaan's Etymological Dictionary, the possible Greek cognates are ἠικανός, "singing early", as in the case of a cock; or κανχή, "noise".)
According to Lewis and Short, cantare can also be used for music that isn't vocal, but they note:
Less freq. of instrumental music, and only with abl. of the instrument (cf. cano)
Cantare may also include such things as the sounds of birds or fowl, as well as enchantments, charms, incantations.
According to Lewis and Short, canere includes many other things that aren't usually associated with cantare. Canere may include, besides the sound of birds, that of frogs as well. It can also mean such things as to rehearse, recite, prophesy, foretell, predict, celebrate, blow, sound and resound.
Cicero, for example, used canere in the more general sense to speak of the playing of flutes:
Si ex oliva modulate canentes tibiae nascerentur, num dubitares, quin inesset in oliva tibicini quaedam scientia? (Cicero, De Natura Deorum)
If melodiously playing flutes were born from the olive tree, would you not doubt that there exists in the olive tree some knowledge of playing the flute?