I agree that "pending" should mean the paperwork is in the registry office or on its way to/from that registry office...meaning that the seller has taken care of the paperwork and buyer can expect to receive the registration papers in due course.
"eligible" means--to me--that the horse is eligible for registration in the specified registry. To me that means seller should provide the completed application with all applicable signatures, stallion report has been filed, parents are permanent registered, so buyer can send in the paperwork, pay the fee, and hassle free get the papers for the horse.
However....be warned that to some people "eligible" means any one of the following:
-horse has AMHR registration papers and is small enough to be hardshipped into AMHA. Yes, horse is AMHA eligible IF buyer is willing and able to pay the $600 or $1200 hardship fee and get that horse to a location where the appropriate officials can inspect the horse.
-horse has no registration papers at all but is small enough to hardship into AMHA as above. From there horse can be registered AMHR based on his AMHA papers....so be prepared to fork out another $200 + or $400+ for AMHR registration
-horse has AMHA papers (or at least a valid application) and from there can be registered AMHR based on the AMHA registration. This last one is the cheapest of the 3 possibilities.
Personally I think in those 3 situations it would be more honest to specify that the horse is "eligible for hardship" into whichever registry.