A eurobond (spelled in one word) is a bond that is denominated in the currency other than the currency of the market in which it is sold. First eurobonds were dollar-denominated bonds that were sold in London, Paris, and Frankfurt. Since then, many other kinds of eurobonds were floated, most notably, yen-denominated eurobonds sold in Europe. Typically, eurobonds are long-term (at least five years) callable bearer bonds with semiannual coupon and sinking fund provision. There are also perpetual eurobonds, as well as convertible eurobonds (which are usually referred to as "equity-linked"). Eurobonds are typically underwritten (i.e., sold by investment banks on behalf of the issuing company), and issues tend to be large (hundreds of millions or billions of dollars).
A euro medium-term note (EMTN) is a shorter term (usually, 3-7 years) security, usually with a shelf registration and continuous issuance. EMTNs issues are usually small (often under $10 million) and often non-underwritten (i.e., sold by the issuing company directly to investors).