This topic often confuses people.
A PDF document itself is not a vector file. However, a vector file/image can be "embedded" within a PDF document.
This begs two important questions - how can you tell if the embedded file is a vector or raster image, and, are there any considerations to consider when a vector file is embedded within a PDF document?
First, one of the easiest ways to tell if the image is raster or vector, open the PDF document in Adobe Reader. Then enlarge the image - enlarge it to at least 600% or more - you will notice either the image starts to distort, or it doesn't. If it distorts, it's raster - if not, it's vector.
Another thing to consider is, if the vector file has transparency. By default, Adobe will open the PDF document with a white background. So not only will you not see transparency, but you will not see anything colored white if it's on the white background. See below for example - you cannot see the top part of the white text.
However, if you change the preferences, you can "Show Transparency Grid" which will then display the white on white, and all areas that are transparent, as seen below:
Hopefully this clears up any confusion regarding vector images contained/embedded in a PDF document. Feel free to ask us any questions using our support page.