1. "lower BB" references a lower bottom-bracket, the part that holds the axle to which the cranks attach.
2. "CX", or cyclo-X is short for cyclocross, which is a style of bicycle race which takes place over varied terrain conditions such as pavement, wooded trails, grass, steep hills and obstacles requiring the rider to quickly dismount, carry the bike while navigating the obstruction and remount.
https://en.wikipedia.org/wiki/Cyclo-cross
https://en.wikipedia.org/wiki/Cyclo-cross_bicycle
The cyclocross bikes appear similar to road racing cycles, the major differences between them being frame geometry, and wider clearances for cx bikes to fit larger tires and generally still function after accumulating large amounts of mud and other debris.
edit: Thank you @jerrycrunch! I've incorporated your bb info.
Sortof. The key defining difference is that a cyclocross bike meets the UCI rules for cyclocross, while a gravel bike doesn't. In a sense, the gravel bike trend is the result of consumers rejecting the UCI's definition of what an off-road-capable drop-bar bike should be.
That being said depending on your leg length to upper body torso length you can of course size a cyclocross bike up or a gravel bike down and achieve sort of the same effect. In my opinion these types of geometry questions do not come up nearly enough in relation to the rider, however, as someone with a very long torso is going to be quite uncomfortable with a bike with a short top tube even if the "size" of the bike is correct for their leg length / height. And of course the opposite can also be true. Ideally we should be sizing and matching frame geometry to the persons geometry regardless of the intended use case of the bike.
That so called nervousness is greatly overstated. I think this is a US thing actually.
As I said, that so called nervousness is overstated because people overthink it. BB height matter but for the most part we intuitively and inconsciously accounts for it and adapt. Also the difference is minute, from a 5 mm to 15mm. It is not like we switch from a road to a tall bike either. And guess what? A tall bike is pretty easily rideable, there are even people doing offroad on them.
edit: Realized it is for turning radius
It doesn't matter much anyway and CX bikes from US brands had already started lowering the BB of the CX bikes because US courses designers are usually less keen on putting off cambers section than euro courses designers.
The explanation I heard for the traditionally higher brackets is that it facilitates quicker turning. Is there truth to this or is this more of a marketing thing?
The rest is mostly the ability to pedal in the corners without clipping a wheel, which help maintain and feel grip, tradition and also to help on the many off camber sections the courses used to have.
I think quicker turning has never been the true reason imo.