"I had so far gathered that for a block to be called a "butcher block," the grain must be perpendicular to the surface".
It refers to both end grain and edge grain.
The ones for butchering or chopping typically are end grain and are more forgiving or self-healing, they will not show blade marks as readily or be as damaged by the knife/cleaver blade.
Butcher Block Wikipedia
"Butcher blocks have been used in butcher shops for centuries, and
still are in many European countries. Increasingly, though, butcher
block is being used in domestic kitchens as an alternative to stone
and laminate countertops. This has created a new industry in the
kitchen design arena and many furniture manufacturers and hardwood
flooring companies are getting into the production of butcher blocks
and butcher block countertops, in part because the countertops can be
constructed from left-over wood that would otherwise be discarded."