If a girl says she'll text you next will guys actually wait until she texts you?

I was texting this guy and I said goodnight I'll talk to you tomorrow, the next day I completely forgot and ended up snapchatting him later, do you consider snapchatting as communicating or is text better?
He usually texts me of a night but since that night he hasn't and I'm thinking that he hasn't since I said I'll text him first, do you think he's waiting or he's just leaving it?
we've spoke in person but haven't texted each other, do I start the conversation or?
i'm just really confused and need a guys perspective on this
If a girl says she'll text you next will guys actually wait until she texts you?
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