Is there a specific difference between the nouns "strip" and "stripe", especially in the context of "a strip(e) of paper"? Are both equivalent or do they carry specific meanings?
A stripe is "a long narrow band or strip, typically of the same width throughout its length, differing in color or texture from the surface on either side of it", and a strip is a "a long, narrow piece of cloth, paper, plastic, or some other material".
These two definitions are not very different from each other, but one must take into consideration the fact that a stripe is in fact a strip with a color or texture difference from the surface (in this case, paper) on the other side of one side of the paper. (Being a mathematician, I can't help but add - these definitions are not accurate for a Mobius strip!).
Reference: Strip, Stripe. 2013. Oxford Dictionaries. Oxford University Press. 27 January, 2014.
"strip" has several meanings. One meaning describes the form of something: something that is long and small. You can speak of a strip of paper, cloth, metal or a strip of land, as already said.
"stripe" is a colour design. A shirt can have stripes, a flag can have stripes. The US-American flag is called "Stars and Stripes".