I don't think my messages are sending right?

I have been texting this person for a few days back and forth fine while I'm on wifi, but when it changes to cellular, I don't think the messages are sending! This persons messages come in as text message but mine are sent as imessage, is that the problem? And I keep trying to send to this person but they don't answer so I dont think they are getting them because I was getting messages from them! Help please!