The two examples you have given aren't comparable. Allow me to explain. "I stopped to smoke" = "I stopped for a short time so that I could smoke." "I stopped smoking" = "I stopped smoking and don't intend to smoke agan." --- "Try to sleep" = "Have a go" / "Have an attempt" at sleeping. It means... "Do your best to sleep". It's ALMOST a command. "Try sleeping" = It's more of a suggestion or a recommendation. Mr X: "Sometimes I feel drowsy in the afternoon, maybe it's because of caffeine or something" Mr Y: "Try sleeping" / "Try sleeping more." ----- The two examples you have given aren't the same at all though. To put your "smoking" example into the second sense, you should say: "Try to smoke" = "Do your best to smoke". [Like, "try to sleep"]. Or ..."Try smoking" = "Why don't you have a go at smoking?" [Like... "Try sleeping.." ... it is a recommendation or suggestion]. ----- Likewise, "I stopped to sleep" = "I waited a moment so that I could get some sleep".[Like, "I stopped to smoke".] OR: "I stopped sleeping" = "I stopped sleeping. I don't know if I will ever sleep again". [Like, "I stopped smoking".] --- The examples you have given aren't parallel at all.... I hope this helps anyway, Take care and good luck!

I try to sleep and I try sleeping; no difference in the meaning, but in grammar yes, one is using the infinitive, and the other is using the gerund