Hi Paul. Here's my take on the topic in general. Others may see it slightly differently and offer other views.
As Dancing Bear says, it refers to the quenching medium you should use when you want to harden a part after machining it. Water and oil will cool the part at slightly different rates. Oil will cool slightly more slowly, which has the practical effect of causing somewhat less warping of the part. For any given part, this may or may not be important. It may also somewhat reduce the possibility of stress fractures, again depending on the shape of the particular part, this may or may not be a concern.
The composition of oil-hardening steel lets it harden properly with the slower quench, whereas water-hardening needs the faster quench. Oil-hardening steel is generally more expensive than water-hardening, but in a home shop the amount used isn't likely to make that a significant issue.
A good reference to all this is the book "Tool Steel Simplified" published by the Carpenter Steel Company. It uses the proprietary Carpenter Steel Co. names for the different types of steel, but you can generalize it pretty easily. I don't think it's still published, but used copies aren't too hard to find. Its general premise is: start with water-hardening. If your application needs the special properties given by oil-hardening (or air-hardening, or shock resistant, or wear resistant, or whatever), then select the variety of steel that will give the properties you need. But the starting point is water-hardening. If there is no particular reason to use something else, use water-hardening.
At least that's the industrial approach. As mentioned, in a home shop the cost savings aren't likely to be an issue, so you might want to standardize on oil-hardening for simplicity.
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