In the code I've written, I receive a delta between two position vectors, I then limit this delta by a maximum delta and return the value. To be clear: the direction of the vector remains the same, only the length changes.
I'm not well versed in mathematics, so my explanation and title may not clearly describe the problem to a mathematician, feel free to improve my text.
I assume that by delta between two vector you mean their difference. Then the operation you are describing is called normalization of the resulting difference. In symbols, you could write it as $$ \frac{v_2 - v_1}{\| v_2 - v_1 \|} $$ where $v_2 - v_1$ is the difference between the vectors $v_2$ and $v_1$, and $\| \cdot \|$ denotes the norm (i.e. length) of a vector. The result will have norm $1$ and you can rescale it simply by multiplying it by the desired length.