Yes, the correct translation for to cancel highly depends on context and speech register.
A good start in the right direction is to reverse-translate the German translations for cancel.
absagen
-einen Termin ~ (Akk. to cancel an appointment)
-ein Event ~ (Akk. to cancel an event e.g. die Band hat ihren Auftritt abgesagt, a colloquial form would be abblasen )
-ein Treffen ~ (Akk. to cancel a meeting)
-einer Person ~ (Dat. to cancel a meeting with a specific person e.g. Ich war heute mit Tim verabredet, aber er hat mir abgesagt.)
Note: Absägen (ab + sägen) literally means to saw off. Colloquially it is used to say a person was fired from a position or in a break up e.g. "er hat sie abgesägt" (he broke up with her)
streichen
-die Flüge wurden gestrichen (the flights were cancelled)
stornieren
-this is a rather formal verb, you use this only for payed services and can usually expect (most of) your money back. Another fitting translation might be to refund which implies cancelation
-Ich habe meine Tickets storniert (I cancelled/refunded my tickets)
-Ich habe den Auftrag storniert (I cancelled the comission)
kündigen
-to cancel a subscription
aufheben
-in this context it means to cancel a contract (einen Vertrag aufheben)