I consider Afro-Eurasia as one giant continent, (same applies to the Americas). However, Asian I believe is a separate term, like European and African. I define Asian as Japan, China, the Koreas, southeast Asian nations. I define India as a subcontinent, and view them as similar, but different from Asians. I view the Middle East/Arabic world as separate from Asia and India, but similar. Europe is different all together culturally, which gives it the title of "Cultural Continent". The same label applies to India, the Middle East, and Asia, as well as all the different parts of Africa (Southern, Northern, Eastern, Western).
The Americas are divided into two "cultural continents"'; The largely Anglo-Saxon north (throw in some Francophones too) and the largely Hispanic south. They share a history of colonization and struggle.
