Hi Samuel,
I am not sure they arise from either of those locations exactly.
Anatomically they are in the medial aspect of the popliteal fossa in a bursa located between the medial head of gastrocnemius and the semimembranosis distal tendon which inserts onto the posterior tibia.
I have attached a typical appearance for you.
This is one I scanned the other day. It is interesting as it contains a loose body as well as synovial proliferation from synovitis.
Steve.