Understanding that underlying infra, when you go deep enough, may have been shared between Gmail & Inbox, same is much the case for all email services anywhere; it IS the front-end UI, and featured enabled by it, that by and large makes an email product.
Marketing at the time seemed to indicate and place Inbox as a separate product, and more than one note from Google hinted that it would replace Gmail. In hindsight it obviously didn't happen, but many of us thought it presented a significant risk to Gmail; just as recently people were looking for "Inbox alternatives" due to its demise, at the time we were searching for "Gmail alternatives" due to potential replacement by Inbox (which I think was a brilliant idea and potentially implementation - but I'm too much of a control freak to utilize:).
I felt Gmail was at _significant_ risk when Inbox was announced; result was unexpected.