OEIS sequence A108070 describes
Number of fusenes with n hexagons.
OEIS sequence A000228 describes
Number of hexagonal polyominoes with n cells.
These sequences first disagree at $A108070(7) = 339 \neq 333 = A000228(7)$.
Given the definitions of fusenes and of polyhexes, it appears that all polyhexes are fusenes.
What are the six $7$-fusenses that are not $7$-polyhexes?