Yes, spastic still has one pretty much unused (in the US, at least) definition that refers to people with CP. The primary definition, though, refers to jerkiness or irregularity usually related to spasms. Spasms and the jerkiness or irregularity related to them are NOT the sole province of CP patients. As such, the term “spaz” is not a reference to CP, but rather to the fact that someone seems to have little to no control over his or her movements, as if he were having spasms. (Small hijack: when I was in grade school, the preferred term was “spaz-moid”.)
The same words or gestures can mean very different things in different societies. The phrase “pick up some fags” is going to mean very different things in the UK and here. There, it’s generally taken to mean buying cigarettes. Here, it’s generally taken to mean finding homosexuals to take home. (We won’t even get into my first thought when I came across the term “eating a fag” in a British novel.) The gesture where you put your thumb and forefinger together with the other fingers extended up? Here, it means “all right” or “good”. Other places, I’m told it means “fuck you”. If someone from the latter culture comes to America and gets that gesture, it doesn’t mean that Americans are rude, offensive people too ignorant to know what the gesture really means. It means that you have to take such things within their cultural context.
Within this cultural context, the word “spastic” hasn’t been commonly used with reference to CP in fifty years or so. It’s just not what the word means to us anymore. Just like gay doesn’t mean “light-hearted and happy” anymore. Sure, that’s still a definition of the word, but it’s not a definition people actually use in this day and age. Language is a fluid thing, and it changes constantly. That’s how we come up with such different meanings for words like fanny, bum, vest, knickers, fag, flat, etc.