Ruler vs Straightedge
Ruler and straightedge refers to tools or instruments which are used to measure length or check if a surface is flat and draw a straight line. Though the word “ruler” has other meanings, and “straight edge” was one of the hardcore punk groups, herein, we will discuss a ruler which is an instrument used to measure length and a straightedge which is used to draw straight lines.
Straightedge
A straightedge is a wooden or plastic instrument used to draw straight lines. It is used to serve as a guide to check if the surface is flat. They are used in industries like the automotive industry and machining service. They are used to check the flatness of machine surfaces. It could be the side of a ruler, book, or a piece of paper. This can only be used to make straight lines but not to measure with. It has no gradations or markings which can help measure the length of a line. It does not have two parallel lines; it is just a straight line or edge.
Source
http://www.rpdp.net/mathdictionary/english/vmd/full/s/straightedge.htm
Ruler
A ruler is a kind of straightedge which has measurement gradients. The measurement could be centimeters, millimeters, or inches, or all measurements together in one ruler. These measurements are marked on both parallel sides of the ruler and are used to measure length. It is used specifically as a measuring instrument or tool. It is also called a scale. They could be triangular or flat.
Source
http://www.google.com/search?q=photos+of+ruler&hl=en&safe=off&prmd=ivns&tbm=isch&tbo=u&source=univ&sa=X&ei=5ezsTY-BFMLTrQfM9ZHfBQ&ved=0CCAQsAQ&biw=1680&bih=929
Source
http://en.wikipedia.org/wiki/Straightedge
Summary:
A ruler can be used as a straightedge, but a straightedge cannot be used as a ruler.
A ruler is a type of straightedge which has measurement gradients and is used to measure length. A straightedge is used only to make or draw a straight line but not to measure the length as it does not have measurement gradients.
A ruler has two parallel lines or edges which have centimeters and millimeters on one side and inches on the other. A straightedge is used only to check if a surface is flat or making straight line. It is a single line not two parallel lines.
A ruler is usually used to draw different geometrical figures as the measurements are specified for drawing it; whereas, a straightedge is not used to draw geometrical figures except for lines that are without a specific measurement.
Rulers can be flat or triangular.