Each product line is a bit different. But for all of them we have a “spur reject” mode (under settings) where two different LO frequency results are masked together to eliminate most spurs. For measuring CW signals this is a good approach, but you lose the real-time nature of measurements in this mode.
The BB60D, being a double conversion superhet, will probably have the most consistent behavior across frequency.
Also keep in mind the BB60D spur shown is -77 dBm. Your bottom picture has a spur of -78 dBm, you just don’t notice it because of the noise.
Edit: I should add that all of our spectrum analyzers, in real-time mode, use a larger set of LO frequencies than sweep mode.