score:13
I'm sorry, but your question doesn't make a whole lot of sense to me. Many, many izakayas, including all the large chains I know of (Watami, Shirokiya, Tengu etc) consist entirely of private booths of various sizes, with service direct from kitchen to booth, and thus don't have a "bar" in any sense of the word, much less bartenders standing behind it.
An izakaya is literally a "stay-sake-shop" (ε± ι ε±), meaning a place that sells alcohol for consumption on premises. And because you traditionally eat while you drink in Japan, izakayas serve food, and I'd even posit that this is the dividing line between a izakaya and a (Western-style) bar, not the location or presence of the bar.
Delineating where an izakaya ends and a restaurant starts is an even tougher exercise. I like @TheWanderingCoder's definition of izakayas being primarily for drinking, while restaurants are primarily for eating, but even that can be a pretty fuzzy line in both directions: there are plenty of "gourmet izakayas" that would be restaurants if they called themselves that, and (for example) yakiniku grilled-meat restaurants that also offer all-you-can-drink deals and are primarily intended for people who want to get hammered.