In addition to dynamic range, SA receivers typically have better harmonic/spurious/image performance than VNA receivers. This is nontrivial and usually involves tunable filters / filter banks and multiple conversion steps, but it is worth the trouble for a SA: when you see a signal on a well-designed SA you can generally trust (maybe to 60dB) that the signal is really there and not an alias of something off-screen. Attenuators and preamplifiers are also common to deal with large/small signals and improve matching. These things are less important in a VNA: if you control the stimulus amplitude, you can probably live without attenuators and preamplifiers. If you control the stimulus frequency, you don't need 60dB of preselector attenuation at the image frequency. Therefore, VNA receivers are typically much simpler than SA receivers. Which is good, because you typically need 4/8 of them, and multiplying the filter banks of a SA by 4 or 8 would get very expensive indeed.
I believe there is an option to buy attenuators and noise receivers on the high-end Keysight VNAs, but you pay a pretty penny for it
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I've also seen a "Spectrum Analyzer" mode that uses Software Image Suppression on the VNA receivers, but I would warn that SIS usually comes with gnarly fine print (like "no signals within such-and-such bandwidth of each other"). It's convenient if you know what you're doing and a real foot-gun if you don't.