Wheel Grinder is much like a wheel lathe. Both are used for truing up (getting rid of flat spots and other uneven wearing of the wheel tread) of locomotive and/or car wheels.
For steel wheels a cutting tool is used for this purpose. Much like you would use on the engine lathe in the school metal working shop (if they even teach that kind of stuff these days).
You cannot use a cutting tool on cast iron, instead you use an abrasive block. Thus you call this work grinding. For a wheel grinder the work turns and the block is stationary. Think of the small shop grinding wheel -- but turn the concept the other way around.
Both wheels on the axle are always turned at the same time. This makes sure that the two diameters are the same.
The wheels are pressed onto the axle and have an interference fit. Special wheel presses are made to do this work and exert forces rated in tons.
The wheels themselves are made up in foundries. Some railroads like the SP operated there own wheel foundries for a long time. Others bought the wheels from manufactures such as Griffin Wheel which had several plants around the country. If you look at the side of a wheel you will find raised letters cast into the web indicating the manufacturer and the month and year.
Cast iron wheels generally were what was called chilled. This is because the sand mold also contained a metal ring next to the wheel tread. This pulled away some of the heat from the molten metal and caused it to cool (or chill) quicker than the rest of the metal. This produced a harder wearing surface on the tread. Once you wore through the "chill" the metal was soft and the wheel was junked.
So this is maybe more of an answer that you expected.
Brian Norden
PS The oldest wheel set (wheels and axle) that I've seen is one in the Nevada State Railroad Museum. Its casting date is April 1869 -- a month before the CP and UP connected at Promontory Summit.