Correct. The ubiquitous Zerk fitting found in the general world is common. There are different thread and attachment methods for the Zerk. There are straight and angled fittings to make greasing easy. But the end the grease gun goes is common.
Frequently, they are just called a grease fitting.
In the industrial world, the Zerk is pretty common as well but there are other ways to attach grease delivery systems to equipment.
On reflection, there may be some grease fittings out there that are a little bit smaller, or larger than a standard grease fitting, but they aren't very common. When I was working in the paper mill, I remember having to change out some grease fittings on some packaging equipment that we could not get the grease guns to work on.
But, in any case, anything you find at a retail outlet will work on your L-N-L. I do have an L-N-L and am familiar with what Hornady installed on the press.