Do wire oven racks and solid plate oven racks have different functions?
This sounds like you might be talking about a european style oven, which generally has 2 types of inserts, wire shelves and solid trays. Wire shelves are used when you want to cook something that is self-contained, like a casserole, baking dish, cookie sheet, etc. The space between the wires allows the free circulation of air, which is a good thing. 

Trays usually come with a removable wire rack and are used when you are baking or grilling (in the US it's known as broiling) something loose like chicken pieces, burgers or sausages. The tray catches any drips and holds liquids that would otherwise fall to the bottom of your oven and make a very sticky and hard to clean mess. The tray slots into the same grooves as the wire shelves so you can put it on any level. 

In the US many ovens have a separate drawer for broiling which comes with a slide-in tray, it's the same concept except you usually can't use the tray in the oven as the sizes don't match. 

Here's a picture of the type of oven I mean, on the bottom you see the tray, on the top the wire shelf.