Dear Sister Sonia,
Please remember a universal law about languages. A second or third person (singular or plural) grammatically uses the male gender unless a particular female or group of females is being referred to. Therefore, Muslim or Mu'min will include women as well.
The details can be very long indeed. However, I will keep it simple and brief, as you rightly desire. This is the understanding of a humble student of the Qur'an.
The term 'Mu'min' derives from the root word, 'AMN'. We can enumerate countless virtues of a Mu'min, but, a brief and simple definition derived from the Glorious Book should be sufficient.
The simplest definition of a Mu'min, of course, I have based it on the Qur'an. Intrinsic evidence with an extrinsic example makes it very easy to understand.
***A Mu'min (believing male or female) is the one who is a source of peace and tranquility. For example, if my Mu'min brother Mubashir tells me that he would do a certain thing tomorrow, I will relax peacefully knowing that he would certainly do it.
Condensing it even more, ***Mu'min is a person who always keeps his word.
My Mu'min Brother Mubashir,
The difference between a Mu'min and Muslim is very easy to describe right from the Qur'an.
***A Muslim is one who submits to Allah's commands and practically surrenders to the constitution of the Quranic state. [His continued submission will soon result in him becoming a Mu'min.]
***A Mu'min is one whose IMAN (Conviction in the Truth) has entered into his heart. [Such a person will not willfully violate the Quranic injunctions.]
49:14 The Bedouins say, “We have attained belief.” Say (O Prophet), “You have not yet attained belief.” Rather (they should) say, “We have submitted to the System” since IMAN (Conviction in the Truth) has not yet entered into your hearts. Yet, if you obey God and His Messenger, He will not diminish in the least the reward of your deeds. Surely, God is Absolver of imperfections, Merciful.”
A lifelong student