spectrun analyzer for the scope differences?

Hello, there are quite a few spectrum analyzer schematics for the scope out there.
The usual schematics use the scope in the XY mode, like this http://www.qsl.net/va3iul/SA/spectrum_an.html
Recently I have found another schematic that does not seem to use the scope in the XY mode but in notmal mode.
Could you please confirm this, or am I missing something?

I believe the trigger output from the scope starts the sawtooth and it "scans" the whole input spectrum, effectively displaying the output amplitude at the scope tube at each time. Am I right?

What are the advantages and the disadvantages of this technique?

The other way around, the circuit triggers the oscilloscope. That's the most simple way. You could send out the ramp voltage to the X-input, there's no big practical difference between both modes. In triggered Y-t you have to adjust the time base, in X-Y the X gain.