Would orc PCs be a subrace of half-orc?

@MFBurrittmechanically, would “full” orc PCs be a subrace of half-orc (i.e. mostly the same but w/aggressive)? sorry if redundant Orc would be its own thing, just as elf isn't a subrace of half-elf.

— Jeremy Crawford (@JeremyECrawford) April 20, 2016