This is the content of a Hadeeth from the holy prophet PBUHH, which says:
رسولُ اللّه ِ صلى الله عليه و آله: المُسلِمُ مَن سَلِمَ المُسلمونَ مِن لِسانِهِ و يَدِهِ
a Muslim is one the Muslims be safe of whose tongue and hand
and also from Imam Sadiq PBUH as:
الإمامُ الصّادقُ عليه السلام: المُسلمُ مَن سَلِمَ الناسُ مِن يَدِهِ و لِسانِهِ ، و المُؤمِنُ مَنِ ائتَمَنَهُ الناسُ على أموالِهِم و أنفُسِهِم
a Muslim is one the people be safe of whose hand and tongue, and a believer is one people feel safe to entrust their goods and lives
and yet again from the holy Prophet PBUHH as:
قـالَ النّبِيّ صلي الله عليه و آله: اَلْمُؤْمِنُ مَنْ اَمِنَهُ المُسلِمونَ عَلى اَمْوالِهِمْ وَدِمائِهِمْ وَالْمُسْلِمُ مَنْ سَلِمَ الْمُسْلِمُونَ مِنْ يَدِهِ وَ لِسانِهِ، وَ الْمُهاجِرُ مَنْ هَجَرَ السَّيّئاتِ
a believer is one Muslims feel safe to entrust their goods and bloods (lives), and a Muslim if one Muslims be safe of whose hand and tongue,
and an immigrant who forsake is one who forsake what is the wrongdoings ...
and maybe there are more ...
Also note that the very wordings might sometimes be somewhat doubtfully exactly what the original reciter has stated ... By the way, Islam is the religion to be Tasleem (submit to Allah), so being a Muslim means being aligned in such a system. A Muslims might be a believer or not, but a believer is indeed a Muslim, as being a Muslim is more general and being a believer is more specific.