I have a 220v line going to my hot water tank do I need to run another line to get 110v for my washer

Yes, a separate dedicated 20 Amp circuit, with #12 wire and a 20 amp breaker.

I have a 220v line to my water heater I need to install a 110v plug from the 220v line for my washer

You likley do not have a neutral line going to the water heater. Whay color wires and how many run to the heater?

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