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When you leverage the brand name/equity to produce a similar product, eg Coke came up with a spin off called Diet Coke instead of making a completely new brand with less sugar content.
Brand extension it´s the activity to use of the brand to other versions of products/services, either directly or indirectly, in order to facilitate the launching of new alternatives or protect/reinforce the existent brand.
Examples, Walt Disney with their merchandise or Sea cruise. Other, bottled plain water with aromas flavours.
Brand stretch it´s the using of the brand to create and distribute in different activity sectors, that the company is not used to be present or even it´s not specialized, unrelated products/services that are not directly attached to the original brand concept.
Example, the 007 perfume brand.
Check this site Colleen, has some good examples:
"The best and worst in brand extensions"
http://www.adweek.com/news/advertising-branding/best-and-worst-brand-extensions-146966
