I think you should be careful about taking analogies too literally in physics - wave functions in basic QM are kinda like probability distributions, for instance, but they are complex valued and change when you sample from them. So they actually behave very differently.
The best way to grok the models more deeply (in my opinion anyway) is to dive into the maths!
The best way to grok the models more deeply (in my opinion anyway) is to dive into the maths!