Yes to both questions. New regulations come out all the time though. I can only speak from my experience, Marines, so any other branches feel free to share your regs.

You'll never see a Marine in cammies at the airport (unless they're transiting under orders) like you see Army because the cammie/fatigue uniform is considered a working uniform only and generally not allowed for wear outside of the immediate work environment. Although you're ok to get gas if needed, and a few other minor exceptions, but for the most part it's a no go off base. A lot of it can depend on your individual command as well. For instance, at my last duty station while under official Marine policy of the time you were technically allowed to stop for gas in cammies on the way to/from work if a NCO/SNCO (higher ranking enlisted) caught you actually inside the building in cammies, more than likely you were guna catch an ass chewing in a gas station parking lot. Which is generally a pretty fun experience as long as it's your buddy getting his ass chewed.

Service and dress uniforms are typically the only ones Marines are allowed to wear in public. But there are some setups that are for official Marine functions only and are not allowed to be worn in public for sorta the opposite reason that you can't wear cammies. Dress blue Alphas, the stereotypical dress uniform you likely see in most recruiting posters, are the dress uniform worn with medals instead of ribbons (ribbons make it dress blue bravos) and typically are reserved for the most formal of military functions.

Sorry for the novel, but here's a link if you really want to bore yourself to tears with Marine uniform guidelines. http://www.marines.mil/Portals/59/Publications/MCO%20P1020.34G%20W%20CH%201-5.pdf Hope this answered your question and feel free if ya got any more.