Are they back because they miss me or because they're bored?

When someone comes back, the first messages sound much the same whether they're driven by love, loneliness or boredom. The difference shows in what happens next. Someone who has genuinely changed will be consistent, patient and willing to talk about what went wrong. Someone who's bored will be warm when it suits them and fade again once they have your attention. Give it time, and their behaviour will tell you.