I.
A wet dream (or erotic dream) is imagining the sexual act in a dream, and that may happen to both men and women. This dream may be accompanied by emission of maniy or not. If maniy is emitted, it becomes obligatory to do ghusl, but if no maniy is emitted, ghusl is not required.
The evidence for that is the hadith of Umm Salamah (may Allah be pleased with her), who said: Umm Sulaym came to the Messenger of Allah (peace and blessings of Allah be upon him) and said: O Messenger of Allah, Allah is not too shy to tell us the truth. Does a woman have to do ghusl if she has a wet dream? The Prophet (peace and blessings of Allah be upon him) said: “Yes, if she sees water (a discharge).” Narrated by al-Bukhari, 130); and Muslim, 738.
Shaykh Bassam said: What is meant by the phrase [translated here as] ‘wet dream’ is things that the sleeper sees in his dream. What is meant here is: if a woman sees in her dream what a man sees in his dream, such as images of intercourse and the like. If the woman sees that in her dream and finds any discharge as a result of that wet dream, she must do ghusl. As for merely having dreams without any kind of discharge, no ghusl is required, because the Prophet (blessings and peace of Allah be upon him) said: “if she sees water (a discharge).”
See: Tawdih al-Ahkam, 1/297.
Secondly:
Women can tell the difference between ongoing secretions from the uterus and maniy, by recognising the distinct characteristics of each of them.
The maniy of a woman is thin and yellow, and smells like dough, and she feels pleasure when it is emitted, followed by languor (tiredness) after it is emitted. This is in contrast to ongoing secretions from the uterus, which are clear and easily distinguishable for the woman experiencing that. We have previously explained the difference between maniy, pre-ejaculate (madhiy) and vaginal discharge in the answer to question no. 99507.
Thirdly:
If a menstruating woman has a wet dream and sees water (discharge), it is prescribed for her to do ghusl for janabah, so that she can benefit from the permissibility of reciting Quran without touching the Mus-haf, because the one who is in a state of janabah is not allowed to recite Quran, unlike one who is menstruating.
For more information, see the explanation of that in the answer to question no. 91793.
And Allah knows best.