It sounds like you have encountered the confusing 'extra' debug button which the CMake Tools extension places on the toolbar. The C/C++ extension's main debugger, configured via 'launch.json', needs to be invoked using the 'debug' view in the left side panel

(as do other debug extensions such as cortex-debug).
Once a debug configuration has been selected, a debug launch button is added to the status bar. This means that users of the CMake Tools extension will then have two different debug buttons on the status bar, which is confusing to say the least. Presumably in part because of this confusion, the CMake Tools extension has options which can be placed in 'settings.json' to remove the buttons it adds to the status bar, either selectively or all together. This is also a useful way to recover quite a bit of status bar real estate, if you don't often need to use things like the toolchain selector.
To remove all buttons added by CMake Tools:
"cmake.statusbar.visibility": "hidden"
And to selectively remove the debug launch button:
"cmake.statusbar.advanced": {
"debug": {
"visibility": "hidden"
}
}
I would expect most users to prefer the selective option, as things like the build target selector are fairly essential to most use cases.
The underlying issue here is that for some reason the CMake Tools extension does not use the standard extension point for debugging functionality, but instead just places an extra button on the status bar to invoke debugging directly without a configuration entry in 'launch.json'. The CMake Tools extension docs describe this as a 'quick' debug function, which suggests that their reason for this design decision is related to different use cases, although personally I can't really see a clear use case for it. Debugging is by its nature an activity which is highly dependent on configuration, as everything from the choice of actual debug program on down needs to be specified in most cases.