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The original Saber - Multple channels and zones, analog only, no trunking.
System Sabers - added analog trunking capability, increased channel capacity.
Astrosabers - added digital capability.
One more to add - ONLY the Astro Sabers will do both wide- and narrowband analog. There are a few (very rare) Syssabers that were made in narrowband only, but every one I've ever seen was wideband only (5 kHz deviation).
Not all the Astro Sabers are digital, however - it seems that many of the ones I see on eBay these days are analog only...
There are some other differences, a bit more subtle.
Sabers that do features like scan do so via cumbersome menus, while Systems Sabers do it via direct button presses. Astro Sabers, unlike Systems Sabers, will remember scan state through a channel change.
The only Systems Sabers I've seen use the value specified for scan hang as also the hang time for talkback scan; that is to say, you cannot defeat talkback scan without giving up scan hang. This can be problematic if you are using a shoulder mike with the radio inside a coat. Astro Sabers allow you to select Tx mode during scan (and set it to selected channel always).
Systems Sabers only allow one MDC ID per radio, while Astro Sabers allow you to enable mutliple MDC "systems" and select which system goes with which channel. Nice if you have call signs on both the Police and the Fire, but different IDs.
Basically, an Astro Saber programs like an MTSX, while Systems Saber has a unique programming metaphor that isn't as user-friendly as MTSX but way easier to use than the original Saber.