A-spec is the older (2013?) integrated brake/gear system, B-spec is the 2014 forwards integrated system (until C spec 😉 ), you can’t mix and match shifters/brakes between the systems if you want to use a single clamp.
So if your running 2013 shimano shifters you’ll need A-spec brakes to use the integrated systems together, it is a nice system to tidy up your bars after all, especially if you have a suspension lockout lever & or a dropper post remote on your bars too.
Bugger seems I’m incorrect, see here
The new I-spec ‘B’ shifters/adapters are backwards compatible to the old levers (with a special bolt included with them), but the old I-spec shifters/adapters are not forward compatible to the new levers.