If something is "overrated", then expectations for the said thing is blown-up beyond reasonable proportions. Ex: That band is overrated. I had heard for years about how amazing they are, but the drummer couldn't keep a beat with a metronome. To "overestimate" something is to exceed the need for whatever it is you are estimating. Ex: If you bring 100 cups to a party that only has 25 guests, you overestimated the number of cups you needed to bring to the party. It's usually better to overestimate than underestimate.

Overrate : 1- to have too high an opinion of omeone or something 2- to put too high a value on someone or something. Example: In my opinion, Hirst’s work has been vastly overrated. ................................ Overestimate: to estimate sth to be larger, better, more important, etc. than it really is. Examples : They overestimated his ability when they promoted him. The importance of these findings cannot be overestimated (= is very great).

Simply stated: "overate" is related to *opinions* "overestimate" is related to *expectations* Source: American English, self

Don't underestimate him, he's not overrated!

Sounds like synonims to me. Only i can overrate is a verb, and overestimate can be noun and verb