I think your terms are a little confused: the column space of a matrix is, by definition, the subspace spanned by the columns of that matrix.
For example, if you take the matrix of real numbers $A = \begin{pmatrix} 1 & 1 & 5 \\ 0 & 1 & 0 \end{pmatrix}$, then the columns are
$\begin{pmatrix} 1 \\ 0 \end{pmatrix}$,
$\begin{pmatrix} 1 \\ 1 \end{pmatrix}$,
and $\begin{pmatrix} 5 \\ 0 \end{pmatrix}$.
Thinking of these columns as vectors in the two-dimensional space $\Bbb{R}^2$, the subspace they span is the set of vectors
$t_0 \begin{pmatrix} 1 \\ 0 \end{pmatrix} +
t_1 \begin{pmatrix} 1 \\ 1 \end{pmatrix} +
t_2 \begin{pmatrix} 5 \\ 0 \end{pmatrix}$
for all real values $t_0$, $t_1$, $t_2$.
In fact (exercise) this subspace is the entire space $\Bbb{R}^2$.
If we also take, say, $B = \begin{pmatrix} 1 & 1 & 0 \\ 0 & 1 & 0 \end{pmatrix}$, we find that (exercise) the column space of $B$ is the same as the column space of $A$.
But if we take $C = \begin{pmatrix} 1 & 0 & 0 \\ 0 & 0 & 0 \end{pmatrix}$, the column space of $C$ is different from the other two: it's the space of columns $\begin{pmatrix} t \\ 0 \end{pmatrix}$ for all real values $t$.