Islam and Muslim have the same letter root (s,l,m) in Arabic. Islam means “submission to the truth” and Muslim means “one who submits to the truth”. The best definition for both words are mentioned in Quran.
Surah 3. Al-i'Imran, Ayah 83
Al-Qur'an Grammar
أَفَغَيْرَ دِينِ اللَّهِ يَبْغُونَ وَلَهُ أَسْلَمَ مَنْ فِي السَّمَاوَاتِ وَالْأَرْضِ طَوْعًا وَكَرْهًا وَإِلَيْهِ يُرْجَعُونَ
Malik : Are they looking for a religion other than the Deen (religion and Way of Life) of