No. I work on Blaze/Bazel. The vast majority of the code is shared between Blaze and Bazel. Examples of Bazel-specific code include support for Windows and support for external deps (needed for multirepos and interaction with package managers).
My employer encountered lots of basic bugs, like file handle exhaustion, which together with the amount of recent activity in GitHub, suggested to me that there is a lot of new code in Bazel. If it's essentially the same as Blaze as you say, then why the new name?
I was there when the name was selected. It turns out "blaze" suggests speed, which is why it was a popular name for other software, and some of it was registered as trademark.