Both are 22 rimfires. The 66 is a German made Colt 45 lookalike or clone.
The 580 is a single shot rifle with a drop comb. It has two cousins, the 581 and 582, clip and magazine fed respectively. There is also a smooth bore, rarely ever seen
One notable feature of the 580 is that like the model 788, it has a six lug bolt. Not easily seen till you remove the bolt. This has to be an aid to accuracy. My rifle was mfd in 1973 and have not fired it yet as I just bought it. Time will tell.