Yes. JIS X 0208 is not a superset of ASCII. Some versions of this standard include most of the ASCII characters, but not all of them.
A related fact is that a file encoded with UTF-16 or UTF-32 is not byte-equivalent to an ASCII file of the same characters, but since those are not character sets, and since Unicode is certainly a superset of ASCII, they do not qualify as answers to your question.
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