There are various ways to cut grooves in flooring to receive slip tongues/splines. If I need to groove an end butt before I install a board, I use a shop made router table and a simple 1/4" carbide dado bit that looks like these:
To cut a groove lengthwise, you could use the router bit but it will be slow and noisy. Instead, use a table saw with a dado blade and a feathering jig.
To cut grooves into flooring already laid, using the "Easy Groove" for 3/4" is the easiest:
But it's expensive. To the guy who said the bit's groove was too narrow for his spline and he had to mill the spline down. Well, just adjust the depth of the router to make one more small additional cut/pass to enlarge the groove. Pretty simple and easier than making spline thinner.
As to cutting grooves in thinner material, use the two methods I mentioned above for flooring not yet installed. If it is installed, you will need to locate a router bit with the guide bearing above the cutter like these from Amana.