Complementing user6975 from the Portuguese side. There are two other portuguese words that could help to separate the context, but in short, all these worlds can be loosely used and can mean anything. Moreover, never expect semantic precision from vendors of touristic stuff or lovers of the decorative arts. (In spanish there are similar words, but I can not discuss nuances of Spanish):

Mourisco : the Muslims who converted to Christianity after the conquest of Granada; or Iberian artistic styles (mainly architecture) from the Muslim dominated period or influenced by them (today the word may be also loosely applied to any art with arabesques or oriental looking patterns). In Spanish there is a similar word

Mozarábico: a more specific word, it means the Christian people who lived under Muslim rule in Iberia - it may also refer to their dialects, arts or styles, and local church rite. If loosely used the meaning may include the Iberian Muslims too, or be synonym with mourisco. In spanish there is also the word 'Mozarabe'.

Mouro is a much looser word - It certainly applies to the medieval muslim invaders and rulers of Iberia, and to medieval North African Muslims, but it may be synonym with "muslim", depending on context and speaker. It may even be the only word known for "muslim" for uneducated people, often in the past before oil made the muslim word more important and there were no TV or films. E.g., I would expect a early XX century poorly educated person be more likely to know the word "Mouro", from local historical tales or basic history at primary school, than the word "muçulmano" (muslim), that he would not have a reason to hear, unless he reads or studies something about the world. Thus, I have seen old literature just use "Mouro" for "Muslim", as probably the writer would expect more people to understand.

There are place and surnames related to these words e.g., Mourinho (soccer coach), Mourão (Brazil's current vice-president),

Complementing user6975 from the Portuguese side. There are two other Portuguese words that could help to separate the context, but in short, all these worlds can be loosely used and can mean anything. Moreover, never expect semantic precision from vendors of touristic stuff or lovers of the decorative arts. (In Spanish there are similar words, but I can not discuss nuances of Spanish):

Mourisco : the Muslims who converted to Christianity after the conquest of Granada; or Iberian artistic styles (mainly architecture) from the Muslim dominated period or influenced by them (today the word may be also loosely applied to any art with arabesques or oriental looking patterns). In Spanish there is a similar word

Mozarábico: a more specific word, it means the Christian people who lived under Muslim rule in Iberia - it may also refer to their dialects, arts or styles, and local church rite. If loosely used the meaning may include the Iberian Muslims too, or be synonym with mourisco. In Spanish there is also the word 'Mozarabe'.

Mouro is a much looser word - It certainly applies to the medieval Muslim invaders and rulers of Iberia, and to medieval North African Muslims, but it may be synonym with "Muslim", depending on context and speaker. It may even be the only word known for "Muslim" for uneducated people, often in the past before oil made the Muslim word more important and there were no TV or films. E.g., I would expect a early XX century poorly educated person be more likely to know the word "Mouro", from local historical tales or basic history at primary school, than the word "muçulmano" (Muslim), that he would not have a reason to hear, unless he reads or studies something about the world. Thus, I have seen old literature just use "Mouro" for "Muslim", as probably the writer would expect more people to understand.

There are place and surnames related to these words e.g., Mourinho (soccer coach), Mourão (Brazil's current vice-president),