In the context of logo design, a variation is a duplicate of a logo with only minor changes. Minor changes typically include changes to the layout (as shown in the example) and to the color of the logo.
Important to note that a logo variation is not a new logo. It uses the same elements as the original logo and is for use by the same company.
Most logo designers charge extra for variations of a logo to be created.
Thanks to Biz-Logo.com for the logo example.
Vector format is a digital image format that makes use of mathematical formulas rather than pixels to represent images.
The vast majority of logo designers work in vector format rather than raster format and most printing companies require that designs be provided to them in vector format.
The main advantages of vector format for logo design is the ease with which changes can be made to the design and the scalability of the design. As shown in the illustration, raster format images can not be scaled up without significant loss of quality. Vector images on the other hand can be scaled to any size without any loss in picture quality.
Popular vector formats include EPS, CDR and AI.
Thanks to Vector Templates for the image.
Also see raster format