Are all tires that are labelled p205 have the same width?

The "P" designates a "passenger" tire. The 205 is the "general" width, expressed in millimeters. I say general because no two tire manufacturers are going to measure the tire width exactly the same. A single tire manufacturer may even measure width differently depending on the type of tire. There's no hard rule here, but the number is going to be in the ballpark of tread width. Even so, I'd suggest you can expect tire width to be within a couple millimeters of the number on the sidewall, +/-.