Both undertone and overtone have literal and figurative meanings. The figurative meanings of these two words are very similar and usually interchangeable.
Undertone in its literal sense means "a low or quiet voice":
"My wife told me in an amused undertone that the neighbors were arguing again."
"The waiter spoke in an undertone and asked if the meat was cooked enough."
Undertone can also mean "a color that you can see in small amounts":
"The fabric is a rich brown color with undertones of red."
In a figurative way, undertone means "a quality, meaning, etc., that is present but not clear or obvious":
"The memo about recent losses had a sinister undertone."
"The play is a comedy with dark undertones."
"There was an undertone [=hint, undercurrent] of fear throughout the city."
Overtone's literal sense has to do with sounds, also called harmonics, that add color and dimension to a voice or musical note. This sense is somewhat technical and used in writing about music:
"The bell's deep tone reveals high overtones as the sound decays."
A common figurative sense for overtone is "an idea or quality that is suggested without being said directly":
"Their words carried an overtone [=hint, suggestion] of menace."
"The sermon had subtle political overtones."
Finally, overtone can mean "a very small amount of something."
"The wine has overtones of fruitiness. [=hints of the taste of fruit]"