I put up these images a few years ago on the Shooters forum.
With the action closed you can see the cartridge back against the lever cut out. As the lever is lowered and the the sliding bolt moves back the cartridge moves to the rear and the lift raises it and the rim is captured under the extractor.
About this time the lever has lowered enough the link has tilted downwards and the cartridge stop catches the rim of the next cartridge in line in the magazine.
If the cartridge stop is a bit short of shaped incorrectly the rim can jump the stop and the cartridge slides under the lifter and jams the action. With a full magazine there is more tension on the cartridges and they tend to find a way over the cartridge stop when they might not if there is only one cartridge in the magazine.
This is an easy if somewhat time consuming fix. The hardest part is taking the rifle apart for the first time as it is not uncommon for screws to be tight or stuck. Take your time the first time.
You can the set the cartridge stop portion of the link on a steel block and use a flat punch which just covers the tip of the cartridge stop. Two or three mild slaps with a 2lb. hammer is a good start.
Look at the cartridge stop first for shiny or wear spots which which will indicate the direction to wish to push metal. It does not take much metal.
The hard part is the try and fit whichmay take two or three tries.
Winchester Model 94 cutaway action closed
Winchester Model 94 cutaway action open