If you yawn, I might respond by yawning. If you are tense, I might response by becoming tense myself. If you are relaxed, I might respond by relaxing. "The bar has a relaxed atmosphere" and "the bar has a relaxing atmosphere" are both correct. The phrase "a nice relaxed atmosphere" means that something _about the bar itself_ seemed relaxed. Perhaps the patrons are relaxed. Perhaps the bartender seems relaxed. Perhaps the furniture seems designed for comfort, not for appearance. The phrase "a relaxing atmosphere" means that something about the place helps _you_ to relax. Since it is very likely that a place that is "relaxed" (itself) is going to be "relaxing" (for you). So, for most purposes, they amount to the same thing; but strictly speaking the two sentences mean something different.

1. It's a very friendly bar with a nice and relaxed atmosphere. This means the bar itself has an atmosphere that is relaxed. On the other hand, this one below: It's a very friendly bar with a nice and relaxing atmosphere - means that the bar makes YOU feel relaxed I hope this helps. Have a nice day! =D