Is there a difference between "formalism" and "formulation"?

Question

I was wondering if there is a difference between "formalism" and "formulation" when we say things like:

this is the mathematical formalism of quantum mechanics.

and we have also

Mathematical formulation of quantum mechanics.

or

All the same, Gleason’s approach assumes some key aspects of the mathematical formalism needed to connect quantum states to specific measurement outcomes.

or

this is a mathematical formulation of hamiltonian mechanics.

or

the Lagrangian formalism of mechanics.

I know the philosophical type of "formalism" but I dont think it would apply here.

I don't know if this question fits here in this forum or not so if not, let me know.

Answer 1

The term formalism means

A description of something in formal mathematical or logical terms.
Any attempt to disprove the theory of evolution using thermodynamics will require proper formalisms.

However, the term formulation means

A particular expression of an idea, thought, or theory.
compare this complex formulation with Bosch's much more simplistic analysis

So I would say that

This is the mathematical formalism of quantum mechanics.

is about the definition of quantum mechanics in mathematical terms, but

Mathematical formulation of quantum mechanics.

is about a description or example of that topic.

_{From Lexico}

Answer 2

Fundamentally, “formalism” and “formulation” are different words, with different meanings, despite being similar looking, and probably having the same root in the far past.

“formalism” comes from 'Formal' whereas “formulation” comes from 'Formula', if that helps.