You're right in thinking that sparging is just a fancy name for rinsing, but there are two ways of sparging.
Batch sparging is done by adding a batch of sparge water, stirring well, vorlaufing, and then draining into the kettle. Repeat this process again as often as is necessary.
Fly sparging is done by vorlaufing, then dribbling sparge water into the mash and draining it out in a continuous process.
In both cases, you want to raise the grain temperature to 165 - 170F.
Going hotter than this can extract unwanted tannins from the grain, resulting in an astringent taste.
Going lower than this can reduce your efficiency as the sugars are not as easily dissolved at the lower temperatures.
From your description, I assume that you are batch sparging. Adding the batch sparge water at 185F will raise the grain bed temp to 165 - 170F. Give it a good stir, and the sugars will get dissolved in the sparge water. Once the sugars are dissolved, you should be able to drain the wort without any further resting time. Some say that a 10 - 15 minute resting time is beneficial. It won't hurt, but I've never seen any evidence to show that it is necessary.
If you're fly sparging, things are a little bit different. At the start of the sparge, your grain temp will probably be in the low 150's. Dribbling in sparge water will not raise the grain temp sufficiently to dissolve the sugars. In this case, I would recommend a mash out to raise the mash temp to 165 - 170F, and then sparge with a lower temp water to keep the grain temp less than 170F.
hope this helps
-a.