I don't think they originate from different definitions. Concepts in category theory are very abstract on purpose, because it focuses on the main essence of the idea, divorced from any particular application of it. Which will greatly vary, but have a common set of properties.

In Haskell functors are endofunctors in the category Hask. Endofunctors are a special case of functors where the source and result category are the same, and Hask is a category of Haskell types. So essentially Haskell functors are all Hask -> Hask transformations. For example applying "fmap show" to a Maybe Int produces a Maybe String, which are both in Hask.

In OCaml you can treat modules of the same signature as categories. If you look at [1] and look at the example for intervals, you have one category of Comparable modules and another category of Interval modules. The Make_interval functor maps objects from Comparable to Interval.

So it really is the same concept, just different applications, but they follow the same theoretical framework and properties.

1: https://realworldocaml.org/v1/en/html/functors.html