In the wild there are 9 species of lovebirds, some species such as the peach face are very common within aviculture, however others such as the black-collared are rarely seen or available within aviculture.
From this page I will illustrate all 9 species along with the available mutations.
Hopefully this will help you in choosing future species & will greatly help with the identification when you see birds for sale.
As you will see within the nine species of Agapornis species (lovebird) only 2 of the species can be visualy sexed (sexually dimorphic) the Madagascar or Grey headed (Agapornis cana) and the Abyssinian (Agapornis pullaria), wth the remaining 7 species being very much alike (sexually monomorphic).