Fixnums are typically stored inline in data structures (like lists, arrays and CLOS objects). Bignums will be stored as a pointer to an heap-allocated large number. Data has tags and thus in a 64bit Lisp the fixnums will be slightly smaller than 64bit. Bignums can be 'arbitrary' larger and there is automatic switching between fixnums and bignums for numeric operations.
The range varies across implementations: the above values correspond to 60 bits; most-positive-fixnum evaluates to 4611686018427387903 in the version of SBCL I am currently running, which corresponds to 62 bits of data.
