What's the difference between those when somebody said:
- I'll inform you.
- I'll notify you.
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"Inform" means "tell." It means you give someone new information.
For example: "I'll inform you of the score of the football game." Is the same as "I'll tell you score of the football game."
"Notice" is similar to "see." It means you now know something or see something you didn't know or see before.
"I'll notice you in the restaurant." This is the same as "I'll see you in the restaurant."
Also, "inform" can take an indirect object, with "of", but "notice" cannot have an indirect object. You can "inform me of the news," but you cannot "notice me the news."
Notice does appear in OED with the meaning of notify or inform, but it notes "now rare". It does cite a recent quotation:
1997 P. Cornwell Unnatural Exposure viii. 189 ‘I assume you've been inside the house.’.. ‘I haven't. Was a neighbour that did. And when I was noticed about it, I called for Norfolk.’
It's unusual enough to give one pause. However that use could be used in the future tense ("I'll notice you tomorrow"), because one might say "I'll inform you tomorrow."
The normal use of notice is what they give as sense 3 (some of which is marked obsolete):
a. trans. To take notice of; to observe, to become aware of.
b. intr. To take notice; to observe or become aware of what is happening.
d. colloq. not so as you'd notice (and variants): not to a noticeable degree.
e. intr. To be seen, to be noticeable, to show.
In these meanings, particularly the transitive use 3a, it would be grammatically correct but semantically dubious to use notice in the future tense. One would not normally say "I'll become aware of you in the restaurant tomorrow".