Oh, thanks for the correction.

If all the vectors are on the unit ball, then cosine = dot product. But then the dot product is a linear transformation away from the euclidean distance:

https://math.stackexchange.com/questions/1236465/euclidean-d...

If you're using it in a machine learning model, things that are one linear transform away are more or less the same (might need more parameters/layers/etc.)

If you're using it for classical statistics uses (analytics), right, they're not equivalent and it would be good to remember this distinction.