Technically, the difference between a "check" and a "tartan" is that the tartan will contain half tones where the colors blend, and the check will just have color next to color with no blending. Let's see if Google image will allow me to give some visual representations.

This is a tartan (the Rob Roy tartan):


This is a check:


Both use only two colors, red and black. But in the case of the tartan a "third color" is created where the red and black mix. Not so with the check.

That's the technical difference. HOWEVER, in common parlance, "check" is often used to refer to a tartan of very simple design. For instance, if someone asked, "What does the Rob Roy tartan look like?" the likely answer would be, "It's a simple red and black check," even though that is not technically correct.

Some tartans that are commonly referred to as "checks" would include the Shepherd's tartan (also the Northumberland district tartan), commonly called "Shepherd's Check":


The Robert Burns commemorative tartan, commonly called "Burns Check":


Both of the above examples are truly tartans, though they are commonly called checks due to the simplicity of their pattern. However, many people mistakenly refer to any and all tartans as "checks" even if the tartan is not characteristically simple in design. This would be the case of the so-called Burberry check, which is really a tartan. Many people use the terms synonymously, or in conjunction. These seems much more common in the fashion industry than in the Highland Dress indiustry, as might be expected. Doing a Google search for the phrase "tartan check" will come up with all manner of web sites selling "tartan check shirts" and "tartan check skirts" and "tartan check lady's pants," etc.

This is an incorrect usage of the term, on a technical level, but very common it would seem.