The torus is in $\mathbb{R}^{3}$ or $\mathbb{R}^{4}$?

Question

Always I belived that the torus is in $\mathbb{R}^{3}$, but reading about the clifford Tori I read that the Clifford torus is in $\mathbb{R}^{4}$. I don't understand it. Since in differential Geometry I had learned tha the torus is in $\mathbb{R}^{3}$, but now if I consider the tours as $\mathbb{S}^{1}\times \mathbb{S}^{1}$, then it is in $\mathbb{R}^{4}$. How explain it?