These statements are made in different senses. If you have a differentiable function $f\colon\mathbb{R}\rightarrow\mathbb{R}$, the derivative in the sense of single-variable analysis is a function $f^{\prime}\colon\mathbb{R}\rightarrow\mathbb{R}$. If you have a differentiable function $f\colon\mathbb{R}^n\rightarrow\mathbb{R}$, the derivative in the sense of multi-variable analysis is a function $Df\colon\mathbb{R}^n\rightarrow L(\mathbb{R}^n,\mathbb{R})$, where $L(\mathbb{R}^n,\mathbb{R})$ is the space of linear maps $\mathbb{R}^n\rightarrow\mathbb{R}$.