The difference between Vector Graphics and Pixel-based
A vector file will usually have the extension .eps or .ai. Unless you have special software you won’t be able to open this file, however this is the file that your design professional or print vendor needs to ensure the best print quality for jobs. Pixel-based images be saved as a .jpg, .tif, .gif, .png or .psd file. Also, saving a Photoshop file as an .eps file does not make it a vector file.
A vector logo will be the most universally useful to you, your printers and other vendors. When working with a logo designer, be sure that your logo is being created in vector format and make sure you request the final vector files.