Grease is like the consistancy of Butter... very thick and does not drip or run.... Lubricating Oil is very fluid and can be used in places that require the oil to flow around.. such as in a Car engine...

I am not really keen to mechanical terms. :D

Both grease and oil are used for lubrication. However, grease is thicker and doesn't run like oil, at least when we are talking about mechanics. You use grease in some mechanism that is hard to open and maintain and will not be serviced as often as a mechanism that uses oil. Cars use oil because it is relatively easy to change it. Heavy machinery (gears and such) would be harder and more expensive to service that often， so they use grease more often

Many people use either phrase. However, technically, grease has greater viscosity. So generally speaking, even though a particular grease and a particular oil could consist of the same ingredients, the grease will be much thicker and therefore last longer than oil.