iMessages on iPhone5 users

Is it necessary to turn on the iMessage? Currently, my iMessage is off, but the MMS Messaging is turned on. When I text people, I see green texts that I sent, but when others send me texts I see grey. Is that what is supposed to happen? If I turned on iMessage then my messages are in blue I think to other iPhone users. If I turned on iMessage, I see a SMS messaging option, and currently it's set to on. What is necessary to receive/send texts no matter what cell phone provider a person has? Say like taxi cabs send out text messages, do I need to turn on iMessage?

Thanks