Dense negative: right, one that blocks light when you try to look\print thru it.
It does not necessarily mean that the print will end up lighter, after all one can burn in. The degree of density is what distinguishes a negative as being dense - that is, it is uniformly of a density that would be difficult to print thru. If you can't read newsprint thru the most dense parts, then it is getting up there.

Thin negative: One that passes more light thru and has no areas that are very dense.

In printing, one usually employs assorted techniques to overcome the problems each introduce.

If a negative sis VERY dense all over, then exposure is the problem. It is possible that a negative can be overexposed to the extent that even the shortest development times will result in a dense negative. If the thinner areas of a dense negative (which print as shadows\blacks in the print) seem to have the correct amount of detail and can be seen thru ok, then the exposure is correct but the development time is too long. It is the amount of development action that builds up these dense negatives that were correctly exposed.

A thin negative can be created via underexposure and\or underdevelopment. Either one of these can do it or both in combination can. If the negative is uniformly thin, it was most likely underexposed and underdeveloped. If it has no detail in the thin areas at all but some density in the areas that would normally print as a mid or light tone, then it was underexposed and probably underdeveloped.

A thin negative can be salvaged by printing on contrasty paper and doing a lot of dodging. You can employ other techniques like bleaching to create whiteas that aren't in the negative.

Or one can scan the whole thing into, I'd better not go there.

For 35mm\roll film I always felt slightly thinner negatives were better to have than dense ones. Much easier to print from thinner negatives for these small format. They are enlarged so much anyway, that printing thru that extra density just results in even more apparent grain in the print.

Hope I haven't confused things. I'm sure others will explain it better.