From "Answers.com":

The noun Moslem "has one meaning:

Meaning #1: a believer or follower of Islam
Synonyms: Muslim, Mohammedan, Muhammedan, Muhammadan

The adjective Moslem has one meaning:

Meaning #1: of or relating to or supporting Islamism
Synonyms: Muslim, Islamic
Pertains to noun: Islamism (meaning #2)"

THere were earlier forms in the nineteenth century including Musselman, and Mohammedan, both of whioch are rarely used now.

Thus Islam / Islamism relates to the religious beliefs, and Muslim, Moslem to the followers there of. THe two words derive from the same semantic root.

An important distinction is between Muslims and Arabs.

Note, from the same source, the distinction around the term "Arab":

The term Arab originally meant a member of the Semitic race of people of the Arabian Peninsula east of Palestine. They were the nomadic Bedouins of the desert. Today, Arabs live throughout the world, including parts or all of Algeria, Bahrain, Djibouti, Egypt, Iraq, Jordan, Kuwait, Lebanon, Libya, Mauritania, Morocco, Oman, Qatar, Saudi Arabia, Somalia, Sudan, Syria, Tunisia, United Arab Emirates, and Yemen. Some Arabs hold Israeli citizenship. (Note that Iran is not an Arab country. Its roots go back to ancient Persia, with a totally different history and culture.) Although not all Arabs speak Arabic, the language is one of the great unifying and distinguishing characteristics of the people, even though dialects differ from place to place.

It is a common misconception that Islam is a unifying force in the Arab world. Not all Arab traditions are Islamic, and Islam does not unite Arabs. Muhammad once commented, "The desert Arabians are most confirmed in unbelief and hypocrisy." There are more Muslims in Indonesia alone than in all Arab countries combined. Some thirty million Chinese are Muslim. In many countries, Muslim and Christian Arabs live side by side, although it is true that in most Arab countries, Islam is the predominate religion. In the Middle East it is not uncommon to meet Arab Muslims, Christians, Druze, and Jews all living within a few blocks of each other.

During the time of the Crusades in the Middle Ages, it became the custom of Christians to use the terms "Muslim," "Pagan," "Turk," "Infidel," and "Arab" almost interchangeably. Today, the Western "man on the street" usually thinks "Muslim" when he hears the word "Arab." This misapprehension is the result of mistaking religion for culture.

WIkipedia adds:

A Muslim (Arabic: مسلم‎), pronounced /ˈmʊslɪm/, is an adherent of the religion of Islam. The feminine form is Muslimah[1] (Arabic: مسلمة‎). Literally, the word means "one who submits (to God)". Muslim is the participle of the same verb of which Islam is the infinitive.[2] Muslims believe that there is only one God, translated in Arabic as Allah. Muslims believe that Islam existed long before Muhammad and that the religion had evolved with time from the time of Adam until the time of Muhammad and was completed with the revelation of verse 3 of Surah al-Maeda:

    This day have I perfected your religion for you, completed My favour upon you, and have chosen for you Islam as your religion.

The Qur'an describes many Biblical prophets and messengers as Muslim: Adam, Noah (Arabic: Nuh), Moses and Jesus and his apostles. The Qur'an states that these men were Muslims because they submitted to God, preached his message and upheld his values. Thus, in Surah 3:52 of the Qur'an, Jesus' disciples tell Jesus, "We believe in God; and you be our witness that we submit and obey (wa ashahadu bil-muslimūna)."

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