carry, bear, undertake
擔 centers on taking on a physical or metaphorical load: carrying something on the shoulder, bearing a burden, or undertaking a responsibility.
擔 is the traditional form of 担. It combines 扌 (hand) with 詹, which likely contributes the sound and may relate to the idea of bearing a load. The modern simplified form 担 replaces 詹 with 旦.
The hand radical 扌 beside 詹 suggests a hand lifting and supporting a heavy object. Picture a worker using their hand to hoist a load onto their shoulder.
For タン, imagine a tan, strong shoulder carrying a heavy burden: tan -> タン, and the hand 扌 bears the weight.