All three believe in one God and trace their faith to Abraham, so they are called Abrahamic religions. Islam differs from Christianity mainly in that it does not believe in the Trinity or that Jesus is God or the son of God, and from Judaism in that it accepts Jesus and Muhammad ﷺ as prophets.
The fuller answer
Muslims respect Moses, Jesus and the earlier prophets and believe that all of them brought the same call: worship God alone. Muslims believe the earlier scriptures were revealed by God but that people changed parts of them over time, so the Quran came to confirm what was true and to correct what was altered.
In practice there are also many shared values and similarities: prayer, charity, fasting, modesty, a ban on eating pork and on interest, and the belief in angels, a judgment and an afterlife. The Quran calls Jews and Christians 'People of the Book' and allows Muslims to eat their food and marry their chaste women.
Say, "O People of the Scripture, come to a word that is equitable between us and you - that we will not worship except Allah and not associate anything with Him and not take one another as lords instead of Allah." But if they turn away, then say, "Bear witness that we are Muslims [submitting to Him]."
This day [all] good foods have been made lawful, and the food of those who were given the Scripture is lawful for you and your food is lawful for them. And [lawful in marriage are] chaste women from among the believers and chaste women from among those who were given the Scripture before you, when you have given them their due compensation, desiring chastity, not unlawful sexual intercourse or taking [secret] lovers. And whoever denies the faith - his work has become worthless, and he, in the Hereafter, will be among the losers.
This answer follows the mainstream Sunni understanding and is general learning, not a fatwa. Where Muslims differ, the answer says so. Have a question of your own? Write to us.