Identify the type of permutation.

When arranging $n$ distinct items in a circle, the number of unique arrangements is given by the formula $(n-1)!$. This is because in a circular arrangement, rotations of the same arrangement are considered identical.

Here, we have $n=8$ people to be seated at a round table.
Using the formula, the number of ways is $(8-1)!$.

Comparing this with the given options:
A: 8!
B: 7!
C: 6!
D: ⁸P₁

The correct option is B.

The final answer is $\boxed{\text{B: 7!}}$.