What are the two different $mathbb{S}^n$ in the construction of the homotopy group $pi_n(mathbb{S}^n)$ that classifies topological defects?

According to Mukhanov’s Physical Foundations of Cosmology,

Homotopy groups give us a useful unifying description of topological defects. Maps of the $n$-dimensional sphere $mathbb{S}^n$ into a vacuum manifold $mathcal{M}$ are classified
by the homotopy group $pi_n(mathcal{M})$. This group counts the number of topologically inequivalent maps from $mathbb{S}^n$ into $mathcal{M}$ that cannot be continuously deformed into each other.

For example, cosmic strings correspond to the homotopy group $pi_1(mathcal{M})=pi_1(mathbb{S}^1)=mathbb{Z}$, which describes the maps of a one-dimensional sphere $mathbb{S}^1$ into itself in a ${rm U}(1)$ theory.

Question In this map, one of the two $mathbb{S}^1$ spaces (between which we consider the inequivalent maps) is the vacuum manifold of ${rm U}(1)$ given by $$|phi|^2=phi_1^2+phi^2_2=v^2tag{1}$$ where $phi=phi_1+iphi_2$ and $v$ is a constant corresponding to the vacuum expectation value.

What is the other $mathbb{S}^1$ in this case?