In a previous Yabla lesson, we discussed the differences between the verbs anheben and aufheben. These separable verbs also look very similar and have meanings related to the base verb heben, which is usually translated as "to lift," or "to raise," and is the Germanic root of the English verb "to heave."
The verb abheben is usually heard in the context of taking out money from a bank machine or bank account:
Dann erhält man so eine Bankkarte. mit dieser kann man Geld abheben.
Then you receive a bank card. With this, you can withdraw money.
Captions 25-26, Eva erklärt: Bankkonten
Wahrscheinlich haben Sie Ihren Kreditrahmen überzogen. -Ja, zu viel abgehoben.
You have probably exceeded your credit limit. -Yes, withdrew too much.
Captions 32-33, Weihnachtsfilm: Ein Sack voll Geld
But abheben is also sometimes heard in the context of an airplane taking off or a rocket launching:
Und dann heben wir schon ab.
And then we take off already.
Caption 43, Ultraleicht-Flieger: Der Gyrocopter
Völlig abgehoben, keine Schwerkraft mehr.
Completely lifted off, no more gravity.
Caption 17, Helene Fischer: Achterbahn
On the other hand, hochheben is used in quite different contexts:
Wenn jeder den Deckel hochhebt, dann verdampft doch alles.
If every person lifts the lid, then everything will evaporate, after all.
Caption 33, Marga Engel schlägt zurück: Die neue Köchin
Die Frau hob das schwere Paket mit einer Hand hoch.
The woman lifted up the heavy package with one hand.
Friedrich hob die Arme hoch.
Friedrich raised up his arms.
Both meanings of abheben are very common, as abheben is both a transitive verb (etwas abheben, which requires an object, usually meaning "to withdraw money) and an intransitive verb ("to take off," which does not allow for an object). Then there is the transitive verb hochheben, which means "to lift or raise something up."
Go to Yabla German and see the two verbs used in different contexts, and go to the Duden dictionary to read the full definitions of abheben and hochheben, noting the ways that the verbs can be conjugated.