I noticed this when the different mods came out and I found I had them in the cup10 folder which made them look like you're describing problem. After I switched them to the other mod folder they were okay.
i have the patch installed.....and it has the driver graphics on the outside of cars.....another person mention different mod folder ...how do i do that?
1st...just because you found some 'paints' online does not necessarily mean that they will work with the models in your game. When people use the term 'mods' they are referring to 3rd party add-ons for NR2003. Some, but not all, of these are GNS (Grand National Series), CoT (Car of Tomorrow ~ both winged & spoiler editions), Trans Am, CTS (Craftsman Truck Series), Hobby Stock, Whelen. When you get into the CoT mods is where it can get confusing as there are, I believe, 4 different versions and some of those have more than one version within itself. Almost all of the 'mods' use different 'models' (the 3D shapes of the cars) and different templates (what is used to 'paint' a car) so they are not interchangeable.
Essentially, you need to find the 'mod' you want to use, download and install it. The 'mod' should place itself within the 'series' folder in, assuming a default install, C:\Papyrus\Nascar Racing 2003 Season\. Inside of the folder for the specific 'mod' there should be a folder called 'cars'. This is where you would place any 'paints' you find and download assuming that they are .car files. If you find flats (the kind you might see posted when asking for a 3D render) then you will need to first convert them to a .bmp or .tga. If you convert to a .tga you can save it in the C:\Papyrus\Nascar Racing 2003 Season\exports_imports folder and use the in-game 'Import' button. If you save as a .bmp you can use a program called WinMip which will allow you to open an existing .car file and edit it by overwriting the existing 'paint'. These are really better left until you get more experienced in the workings and modifying of NR2003.
Now you're probably going to ask, 'Where do i get these mods?'. Well, they're all over the place. One 1st stop I'd recommend for you is MasGrafx and read through their Mod Install Order and pick up what files you can that they suggest. I've always followed this and I've never had a problem with any mod (and I've got 30+ in 5 different NR2003 installs).
I hope this helps you understand the process a little better.
edit: Another place to check out is NR2K3Tracks. Specifically the N2k3 Car and Mod List.