In physics, the Master’s degree is not a common terminal degree except for someone who starts a PhD program and then quits after 1 or 2 years. Typically you don’t pay tuition for a physics PhD program and are on either a teaching or research assistantship.
In electrical and computer engineering, are PhD students typically funded and not paying tuition? What about computer science? If you think you want a Master’s but probably not a PhD, can you apply to a PhD program, fulfill the requirements for a Master’s, and then leave?
Do engineering students pay for MS degrees? Commonly? Yes. Do the majority? No. Should they? Absolutely not. In engineering (or any STEM field) a student should either get a position supported by an assistantship or else go work in industry and let the company pay for their degree, in my opinion. The exception is a 5-year BS/MS, in which case a student paying makes more sense to me.
PhD students are nearly universally funded pretty much across the STEM spectrum. If you don’t think you want a PhD and just want a paid MS, sure you could do what you suggest and lie about it, but that is deeply unethical. It is likely to become obvious to the PI at some point and good luck getting any job seeking support (e.g. references) from the person or people you just screwed over by doing that.
Many MS students in engineering are paid by an employer or are self funded. PhD students in STEM should be fully funded.
Most schools I’m aware of do NOT award MS degrees to PhD dropouts. Most likely for this reason.