Hi there, I’m glad you brought this up, in case anyone else had the wrong idea.
First of all, let me say that Muslims do believe Jesus ascended to Heaven… the Qur’an actually says that God “raised” him up, and not that he ascended. But Muslims believe it was before Jesus (allegedly) died on the cross, and that Jesus is still in Heaven, until he will return in the last days.
Regarding the ascension of Muhammad, it was an event during his lifetime, there is a lengthy hadith which described it in detail–if you’re interested let me know and I’ll try to find it for you. I skimmed the wikipedia article and didn’t see anything obviously wrong, but then again I only skimmed it. Nonetheless, the gist of it is correct–that Muhammad travelled miraculously to Jerusalem and led the prophets (including Jesus) in prayer, and from there ascended to heaven where he was given a tour, so to speak, and the commandment of daily prayers.
Muhammad himself died many years after this event, in Medina, in the house of his wife, 'Aisha, and he was buried there in her house. The mosque in Medina (which is called Masjid An-Nabawi–mosque of the prophet) was eventually expanded (to hold more people) and now it encompasses the grave of Muhammad.
So specifically, it’s not a shrine built around him or his grave, but in the expansion of the mosque, they decided to not move the grave.