Huh? Some differences:
- A formula says nothing about evaluation order, sometimes not even about evaluation (example: where’s the algorithm in e^(iπ) -1 = 0?)
- the computations that an algorithm makes cannot always be expressed in a closed-form expression (example: what’s the formula for quicksort?)
A formula is “a concise way of expressing information symbolically” (https://en.wikipedia.org/wiki/Formula)