The sample variance, s2, is the variance of the sample, an estimate of the variance of the population from which the sample was drawn.

"Sampling variance" I would interpret as "the variance that is due to sampling", for example of an estimator (like the mean). And so I would consider these two terms to be quite different.

But "sampling variance" is a bit vague, and I would need to see some context to be sure. And I'd prefer to say "sampling variation" for the general idea.

[Many people (particularly in quantitative genetics) use the term "variance" in place of "variation", whereas I would reserve "variance" solely for the particular measure of variation.]

You made it right. my students do ask me about this question in AP stats. He is quite ok with the sample variance while not so sure about the sampling variance and we barely use it. But i said to him that for one single sample, among million of others,  you have sample variance, you don't have sampling variance which is incurred when you take one statistic from many samples.