There is actually not much difference between gages and plums. Gages are generally considered to be green to yellow, while plums are red to purple. But there are yellow plums such as Prunus domestica Pershore. And Prunus domestica Jefferson is almost red....
What is certain is that the first "gages" were brought to this country by Sir William Gage in the mid 18th century. They were highly regarded as they were sweet, while traditional english plums were sharp and needed to be cooked before they could be eaten. To this day, there are no cooking gages, and if you look far enough back into the parenthood of the sweeter plums, you tend to find a gage.
So the answer is probably that no one knows anymore, and that the distinction between the two has become so blurred that one could argue for hours which is what provoked this post. Or you just eat them - which is also to the point as our gages and plums are ripening now. We have just been having a run off between Cambridge Gage a gage and Coes Golden Drop a plum. I tell you they were both delicious. We cheat a bit - to get early fruit we train them against a wall and cover with fleece if it gets cold in April. But both are fine in the open - they just crop a bit later.
Off for some more :-)
Relax, watch your plants grow and enjoy!