Eurodollar are the interests that banks outside the US pay: http://en.wikipedia.org/wiki/Eurodollar EuroFX or EUR/USD refers to how many euros you can buy with one dollar (exchange rate).
the relationship (you asked 'relationship' over 'difference') is that interest rates often influence the fundamentals of the fx contract. eg in terms of carry trades. therefore, perhaps you will also want to consider looking at euribor futures (euro equiv of usd eurodollar stir) on liffe as well as eurodollars - perhaps the spread against same maturities to understand the carry bias?
There is no direct correlation between the two, except for the cost of carry (the spread between the interest rates of the respective currencies) imbedded in the currency futures.