Do we distinguish between row and column vectors when speaking of $\mathbb{R}^n$?

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Another question I feel silly for asking: I know that row- and col-vector spaces will be isomorphic, but is it conventional to distinguish between them?

eg if we want to refer to the row-space of the 2x2 identity matrix, are the sets $$\left\{ \begin{bmatrix} 1 & 0 \end{bmatrix}, \, \begin{bmatrix}0 & 1 \end{bmatrix} \right\}$$ and $$ \left\{ \begin{bmatrix} 1 \\ 0 \end{bmatrix}, \, \begin{bmatrix}0 \\ 1 \end{bmatrix} \right\}$$ considered equivalent?

Thanks in advance for your time and assistance.