Is there a distinction between prayer and worship?

I noticed a particular line in the Tashahhud > Salutations to God and prayers and good deeds. **Peace be upon you, O Prophet**, and the mercy of God and his blessings. Peace be on us and on the righteous servants of God. I bear witness that there is no god but Allah, and I bear witness that Muhammad is His servant and His messenger. The bolded section seems like it is directed to Muhammad. This rings a similar tone with some Christian prayers, in which we pray to the saints (people in heaven) but **not** worship them. Like most of Christianity, does Islam make a distinction between prayer and worship?