Yes, Chúa means God, it also means Lord. Trời means Sky, also God. We usually use "Trời" for Sky tho, and when we use it for God, we add-in the word "ông" (Grandpa/He) to make it clearer if there is no context. "ông Trời" = "God" or literally Sky Grandpa! Mặt Trời = "Sun" or literally Sky Face! "Trời ơi!" = OMG!
I'm a little late for this supreme being discussion but could god mean the Christian one as well as the numerous other ones in Vietnamese culture? When I was living in Vietnam earlier this year, I participated in a family tradition of honoring the kitchen god, Ông Táo. The deeper I get in the culture, the more I see there is to learn. When someone dies, it was described to me that the god or king under the earth makes judgement as to how long they stay until allowed to go to heaven. It seems to me that Vietnamese Buddhism is kind of complicated and has many layers.