Verizon service, but t-mobile phone?

no bc verizon is not the same network as gsn phones

No,you can't use Verizon network service on your T-Mobile based Samsung phone.Because your phone supports GSM carrier but Verizon is CDMA.
You will be able to use other GSM network than T-Mobile like 3,rogers etc....If you are interested to swap your network carrier from T-Mobile to other network means,Make sure your phone is unlocked.If it's locked by particular network,you will need to unlock your mobile phone.You can unlock your mobile by network unlock code.If you need an unlock code visit Unlock-Zone.com Here you can unlock your phone at low cost.