Difference between $S^{1}$ and $\mathbb{S}^{1}$

Question

Whats the difference between the two? Or are they both the unit circle? My lecture notes for a topology course use $S^{1}$ for the "circle" in one example and $\mathbb{S}^{1}$ in the next example for the "boundary circle". Is it just a notational inconsistency?

EDIT: Neither is defined in the notes. I infer that the "boundary circle" is $\{x^{2} + y^{2} = 1 \mid x, y \in $$\mathbb{R}$$\}$ from the example. Indeed, $S^{1}$ seemingly denotes the same thing.

Answer 1

These are both used to mean the circle. Probably the non-blackboard-bold one is the more common.