Notice and notification sounds very similar, as both refers to the procss thorugh which the parties can inform each other. However, their meaning is different.
Notice is rather used in the sense of observe or warning, while the synonym of notification could be announcement. And this is the main difference between the two words. It is important to note that notice can occur in this form either as a noun or a verb. If it is a verb, it refers to the meaning of observe. But when it is used as a noun, then it means warning. In other words, notification means a formal announcement or something by which a notice is given, while notice, as a noun, refers to a formal and written announcement, as a verb, it means to comment on something, mention or to become conscious about something. Finally, in legal context, notice means a legal warning in written format.