TBH, there's no simple way to answer this unless you really understand the printing process. I don't know how much or how little you know, but being that you asked the question I will break it down. Here goes.
The Pantone colors you see on your computer only emulate what will actually print once the ink hits the paper. Each PMS color you chose create what's called a color separation in the file, that the Print house later uses to create a screen for their press. Each screen in the print process, allows for one ink to flow through and land on the form, the sheet of paper, fed through the printing press. In 4 color process printing for example, there are 4 separations or 4 colors that make up all the images you see in your finished product: They are called CMYK. Cyan, Magenta, Yellow, Black. In printing with Pantone inks, the technique is the same, it's just the inks that change. If you chose a blue and a yellow, there will be two screens used. If you choose a blue, a yellow, and a red, three screens will be generated. If you mix CMYK and a PMS colors, five, six or seven screens will be generated.... And your print job will be very expensive :)
The important thing to keep in mind is that the printer (the person) can feed ANY inks in their press even after you've released your files. The files you release are only guides that tell them which inks you prefer in your separations.
To make this process easier for the designer, Pantone came together with Adobe among other developers, and created on-screen, RGB versions of each one of their inks to be viewed trough the design programs. The values you see on the screen are again only representations of the finished printed product. To have a more accurate view of what the finished print will look like you need to look at PMS books.
Now that you know that each color represent a screen, or a color separation, I can introduce Paper Quality as another variable to this process. There are a million different paper types out there, but the most common ones are either Coated (glossy-ish) or Uncoated (rougher, matte). Each type of paper reacts different to the inks.
Coated papers will not absorb as much ink and thus leave more color on the surface. They will also reflect more light, so the colors you see in the end look more saturated and deep on these papers.
Uncoated papers absorb more ink into them, and have a rougher surfaces. Thus more of the paper grain is visible and the colors look more muted, and always are bit lighter. Black for example, will look like a charcoal.
Most designers that have been working with paper for a while are aware of this and once they've chosen how they want their finished product to look, use the appropriate PMS library, to avoid misunderstandings when presenting ideas to clients or designing their materials.
Hope this helps, and if I over-explained it is only because I have no knowledge of your experience.