'other than' implies two or more choices that are equally important or that you feel neutral about. Let's say you could either go fishing or go swimming, and you don't have a preference: Other than going fishing, we could go swimming.
'rather than' implies two or more choices with different levels of value or desirability. Let's say you like swimming more than fishing: Rather than going fishing, I would like to go swimming.
Wow -- good question. I can’t really answer it grammatically, maybe an example would help?
”We have to have something in the house other than desserts” (other than = apart or different from)
”We should have healthy foods in the house rather than just sweets.” (rather than = and not)
yes there is a difference other than is use when you are giving out things through some one for example give the white ball to john and other one to peter. while rather than can be use when you want to make choice i will rather have ice cream than tea.