Differences between have been explaing below.
Bakhoor (Arabic: بخور) are tablets made of powdered agarwood chips and other ingredients. These already have a little smell but are soaked in fragrant oils such as oudh, musk, rose, jasmine, sandalwood and other essential oils. They are burnt using charcoal incense burner or an electric incense burner which releases an exotic fragrance upon being burned.
Mabsoos/Mabthooth are shavings of agarwood chips. They already have a little smell but again, soaked in essential oils mentioned above. They can also be mixed with agarwood powder. These can be burnt using charcoal incense burner or an electric incense burner.
Muattar are chips of agarwood, after the oil has been extracted. However, there is still a small amount of fragrance left in them. These are then soaked in essential oils. Again, these can be burnt using charcoal incense burner or an electric incense burner.
It is customary in many Arab countries to pass bakhoor / Mabthooth / Muattar amongst the guests in the majlis (congregation) as a gesture of hospitality.
Muslims use it on special occasions like weddings, Friday prayers or generally just to perfume the house.
Many other religions also use bakhoor / Mabthooth / Muattar during religious services and at houses as a blessing.