A gradient is a type of fill where the fill color gradually fades from one color to another or from dark to light.
Also see solid fill
Graphic design is a collective name for all disciplines related to visual presentation as it applies to business images. The field therefore includes logo design, packaging design, stationery design, decal design etc.
In a grayscale image, each pixel holds only information about its intensity, not its color. In other word the image has no color apart from a range of greys from white at its lightest to black at its darkest.
Note on spelling:
"greyscale" or "grayscale"... It seems the jury is still out on the correct spelling. Both are used often so either would be correct.
Also see final logo files
A popular raster image format for the web. Traditionally GIF has been the preferred format for web logos with limited colors. Recently some designers have started using the PNG format instead.