I was asked what the difference is a while back by a student. Somebody describes it pretty well I think by saying:
“Eine Schätzung ist eine Vorhersage, die auf überprüfbaren Fakten basiert, Raten hingegen basiert auf Gefühlen.” ( An estimate is a prediction based on verifiable facts, whereas guessing is based on feelings. )
I found that explanation on this site
Can you think of more examples? 
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Hmmm… I know exactly what you mean. Sometimes you get asked questions, which is very clear for yourself, but once you have to explain it, it’s getting complicated to find the right words. 
Ok, so I would explain it maybe with these things in addition, although that explanation is already quite good.
Schätzen kommt meistens im Rahmen von bevorstehenden Ereignissen zum Einsatz, z.B. ich schätze, dass ich um 14Uhr nach hause gehe. Raten würde ich mehr im Rahmen von Rätseln oder Aufagaben sehen, z.B. ich rate, dass die richtige Antwort (auf die Frage nach der Uhrzeit) 14 Uhr ist.
(Estimating is used for future happenings like I estimate, that I will come home around 2pm. While guessing is more related to puzzle, tasks and questions, like I guess, that the correct answer (on your qestion for the time) is 2pm.)
Does that make sense for you? 
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Hi @ClaudiP yes thanks that makes totally sense. I agree that “raten” falls more in the realm of game shows and wild guesses.
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