Honeycreeper is kind of a generic term for a number of nectar-eating birds that may or may not be closely related. I don't know anything about African honeycreepers, but those in Hawaii are in their own family, the Hawaiian Honeycreepers. Honeycreepers in the Americas are allied to tanagers.
I think the blue bird in Rolando's image is yet another tanager relative, a dacnis. I lack the appropriate references to be sure of the species, but will check internet sources and see if I can figure it out.
Nancy L Newfield
Metairie, Louisiana USA
USDA Zone 9b