What is the difference between Islamaphobia and anti-Semitism?

I think it has to do with the Holocaust. Everyone is afraid it will happen again, so they are really against saying anything bad about Jewish people. They're also a considerably smaller group than Muslims, so people are more sensitive because they are a minority. Not to mention that people are still freaked out about terrorism. There's a lot of other religions that people are openly prejudiced against. Catholics get a lot of flak, and the Church of Latter Day Saints.