So what is the difference between Lucite and acrylic?
It's simple: Lucite is a brand of acrylic, that's it. Just like Plexiglas, Perspex, Policril, Gavrieli, Vitroflex, Limacryl, R-Cast, Per-Clax, Plazcryl, Acrylex, Acrylite, Acrylplast, Altuglas, Polycast, Oroglass, Optix - they are all brands of acrylic.
Bulletproof glass however is something different, it's polycarbonate.
Anyways, the real reason I love seeing things made of acrylic (even polycarbonate, like at banks) is, in general, they are being held with fasteners and I like that you can see right through the material to see exactly how the fasteners are assembled.