Does fee depend on type of addresses involved into transaction?
Sure. You can see differences.
https://coinb.in/#fees
Fees decreased to
1 sat/byte, temporarily. It's time to move coins with cheap fees, of course, if you don't have urgent need and don't hurry with your transactions. Fees for transaction with 1 input (148 bytes), 3 outputs (102 bytes) costs only 260 satoshis.

Sources:
https://tradeblock.com/bitcoin/historical/6h-f-tfee_blk_avg-01051https://coinb.in/#fees
Fees decreased to
3 sat/byte, temporarily. It's time to move coins with cheap fees, of course, if you don't have urgent need and don't hurry with your transactions. Fees for transaction with 1 input (148 bytes), 3 outputs (102 bytes) costs only
780 satoshis.

Please check more there:
https://tradeblock.com/bitcoin/historical/6h-f-tfee_blk_avg-01051https://coinb.in/#fees
Fees decreased to
2 sat/byte, temporarily. It's time to move coins with cheap fees, of course, if you don't have urgent need and don't hurry with your transactions. Fees for transaction with 1 input (148 bytes), 3 outputs (102 bytes) costs only
520 satoshis. It means the transaction of 260 bytes cost 520 satoshis as transaction fees

Please check more there:
https://tradeblock.com/bitcoin/historical/6h-f-tfee_blk_avg-01051https://coinb.in/#fees