The difference between slick and sleek

Both mean smooth or seeming to be smooth.

To me, slick is more about touch: slippery, and sleek is more about sight/appearance. A wet moss-covered surface is slick. A satin skirt is sleek.

As a metaphorical descriptive, "slick" implies "sexy" (also in the metaphorical sense), and, as with real sex, what is considered "sexy" varies greatly from one observer and context to the next. I might consider a 20 pound bicycle to be "slick", while someone else would apply the adjective to a 1000 pound motorcycle. But the term, absent knowledge of the observer's preferences, implies nothing about the form of the object.

See Urban Dictionary:

slick
  Smooth, cool, awesome. 
  Luke is so slick

"Sleek", on the other hand, is somewhat more objective, though it may also be metaphorical. It refers to the shape and form of the entity, and means, basically, "streamlined" or "smooth and flowing". A fancy sports car will generally be considered "sleek".