Are "cryptarithms" the same thing as "alphametics"?
Not exactly. There is some difference.
Cryptarithms refer to a broad genre of mathematical recreations featuring arithmetical operations, in which the numbers are substituted for letters or other symbols.
Alphametics are a special set of cryptarithms in which the letters make sensible words or phrases.
For example, this puzzle with jumbled letters is a cryptarithm:
M D Y D + Y R Y R ----------- R B M M B
Whereas this other one
S E N D + M O R E ----------- M O N E Y
is also a cryptarithm but of a special kind termed "alphametic" because its letters form words that make sense.