What is the difference between iron and steel?

Iron is an element however it is not found in its pure form and even then it only exists in the lab as it is very soft and very difficult to purify iron to its pure properties.

Iron as the word is use commonly is typcially an alloy of iron with large amounts of carbon and also typcially manganese . Carbon content is typically 3-5% weight and maganese roughly .5-1.5% with other elements randomly present in smaller quantities. Silicon is typcially present in a couple weight percent in cast iron too.

Irons main advantage is that is easier to cast than steel due to the low melting point the result of the high carbon content also reducing the carbon content to get steel then maintaining the higher temperature is expensive compared to iron.

Steel however is much stronger and more ductile thus making it worth the effort to get the carbon out.

A quick info about iron-carbon

Metals and other solids can actually dissolve other elements into a solution . Iron does not dissolve carbon very well at low temp but it's 
solubility abruptly increases around 1000 C to .8 % increasing to almost 2.5% due to a change in the atomic arrangement . Carbon that doesn't dissolve turns into cementite which is an Intermettalic (basically a compound) that is very brittle but also strong. After 1-1.5% carbon steel becomes too brittle to be useful however 2% and up to 4% the melting point is rather low making it easy cast despite the brittle nature. At very high carbon percentages carbon will come out and become graphite making the cast iron ductile.

Realistically high carbon steels and low carbon cast irons are similar . The reason for the different name is diminishing returns . Adding carbon to steel makes its harder and more brittle. At a point it becomes so brittle that any internal stresses or defects cause it to prematurely fail weakening the material. This occurs around 1.5-2% carbon. Materials around that concentration have the manufacturing disadvantages of steel with the low performance of cast irons thus don't really exist practically.