If you want to understand the language of stochastic calculus as mathematicians have formalized it, then you need all of their jargon. Probability, Diff Eqs, Integrals, and Derivatives. If you are trying to tick a box on a resume, then that's what you have to do. If you have a CS degree then you have a little slice of Probability from combinatorics and information theory. You'll have to build up from there.

Stochastic Calculus was invented to understand stochastic processes analytically rather than experimentally. If you just want to build an intuition for stochastic processes, you should skip all that and start playing with Monte Carlo simulations, which you can do easily in Excel, Mathematica, or Python. Other programming languages will work too, but those technologies are the easiest to go from 0 to MC simulation in a short amount of time.

If you just want some intuition, I found this previous HN submission https://jiha-kim.github.io/posts/introduction-to-stochastic-... pretty approachable at giving you some key ideas without being too rigorous. It's not useful for doing calculating anything practical of course but it can either be a starting point or just a way to satisfy that curiosity.