Same word, different contexts and meaning. In ML tensors are multidimensional arrays (and nothing more). Neither physicists nor ML researchers/developers are confused about what it means.
I'm sure this has confused a lot of people, especially beginners. Clashing terminology is one of the main difficulties in interdisciplinary work, in my experience. I don't think it's good to shrug it off like that.
Words can have multiple meanings, but I think we can all agree it's preferable if they don't have multiple slightly different depending on context meanings. That's just confusing.
(Sort of like how vectors kind of got going via a list of numbers and then they found the right axioms for vector spaces and then linear algebra shifted from a lot of computation to a sort of spare and elegant set of theorems on linearity).
Dot product: https://en.wikipedia.org/wiki/Dot_product
Matrix multiplication > Dot product, bilinear form and inner product: https://en.wikipedia.org/wiki/Matrix_multiplication#Dot_prod...
> The dot product of two column vectors is the matrix product
Tensor > Geometric objects https://en.wikipedia.org/wiki/Tensor :
> The transformation law for a tensor behaves as a functor on the category of admissible coordinate systems, under general linear transformations (or, other transformations within some class, such as local diffeomorphisms.) This makes a tensor a special case of a geometrical object, in the technical sense that it is a function of the coordinate system transforming functorially under coordinate changes.[24] Examples of objects obeying more general kinds of transformation laws are jets and, more generally still, natural bundles.[25][26]
Tensors require some algebraic structure, usually a vector space.