Is there a difference between chalice and goblet, other than (maybe) religious connotations on the word chalice?
In the final analysis, the words describe objects which are fairly equivalent.
A goblet is:
a drinking glass with a foot and stem.
A chalice has a broader definition, but this is mainly balanced out by the fact that the third meaning is rare, and the fact that you specified differences other than relating to the first definition:
a.) a cup for the wine of the Eucharist or Mass.
b.) the wine contained in it.
2. a drinking cup or goblet
3. a cuplike blossom
As to usage differences: the terms are both in use, though goblet seems to be the more popular word to use in terming gourmet wineglasses and other goblet-shaped glassware, where chalice has a more rich, historical feel, often describing ornate metal goblets. You might drink out of a goblet, but look at a chalice in a museum, or put it on your mantelpiece.