While running last night I started to wonder if a teleconverter would work but I wasn't sure because although I know you can increase the magnification of a macro lens I wasn't sure if they were essentially a 2X relay lens, I find photographic speak frustrating sometimes...
I know what you mean. In the microscope world, the terms "relay lens", "photo eyepiece", "projection eyepiece" are often used interchangeably, but can also refer to very different optics. It is probably futile to expect this to change.
Generically, I think of a "relay lens" as an optical way to move the location of a "real image" (one that could be seen on a "screen" if one were placed at that image's location in space), to a different location. While doing so, it may (or may not!) change the magnification --either up or down. One reason this may be done is to "size" the image to fit on a specific film/sensor format (which would be your case with a 10X microscope objective and a 24x36mm sensor). In photomicrography, this is the norm. The image formed by a microscope objective hasn't changed much over the years... about 20-25mm in diameter. But this same image has been used on film/sensors as large as 8x10 inches to as tiny as 2.7x3.68mm (1/4" sensor)! It is essential that the objective's image be "sized" or "mapped" to fit the camera's format.
You might glean more info on this here:
In the case of a teleconverter used "conventionally" in general photography, it is to provide a "magnified" view, as if a lens of longer focal were used.
So with this terminology, the context of usage is important. Even then, it can be confusing since different people mean different things with the same words.