Muslims pray to the exact same god as Christians do and they recognize Jesus Christ as a prophet.
They don't actually. I have a degree in Religious Studies (focus on Islamic, Hebraic, Mormon, and Hindu Thought) and a Masters in Christian Thought. As exciting and useful as they sound.
Anywho, Muslims do not pray to the Christian God, neither do Jews or Mormons. In Christianity, one must believe that Jesus is God. If you don't believe that he is God, then you're not a Christian and you believe something else. It's just the reality of the faith and thought.
Muslims believe Jesus was a prophet and not God, didn't die on the cross, didn't die for the sins of humanity, wasn't resurrected. That's nearly as far away from the Christian understanding of God as you can get. Jews hold the same position, though not the prophet aspect, most Jews acknowledge Jesus as a good teacher.
Again, not a big deal to not believe Jesus of Nazareth was God. But, if you don't, then you're not worshiping the same God as Christians do.