Can someone tell me the difference?

Tanzanite is Zoisite. Fancy means nothing in gemological terms.

Mostly marketing stuff. It really depends on how you want to look at things.

Consider this. Zoisite is a mineral with certain properties. One being that it is trichroic. It has three colors each in a different crystal direction. However, after heating the resultant blue/purple stone is dichroic having only two directions of color. The third color having been "burned off". The resultant stone is a dichroic blue/purple color. But, it is still the mineral Zoisite, just altered by heat.

The discovery lore of Tanzanite goes like this. When the deposits of large gem quality Zoisite was discovered in Tanzania, it was after a large bush fire that exposed the bright blue stones. So the original surface gathered stones had been heated, and were now blue/purple dichroic stones. It was soon discovered how to heat treat the Zoisite to achieve this color. It was these blue/purple stones that were brought by Campbell Bridges to Tiffany. Tiffany originated the 'Tanzanite" name to market these stones to the public. So, the term "Tanzanite" originally applied to a blue/purple dichroic stone that was a heat altered form of the mineral Zoisite.

In the strict sense these "fancy colors" are an unheated trichroic form of the mineral Zoisite. This is not what Tiffany was marketing as "Tanzanite". But, since Tanzanite is not a mineral name with scientific meaning, the rules for using it are less rigid. So, I guess it is up to the individual seller to decide what nomenclature he wants to use. The important thing is that he understand the issues, and is able to fully explain them to his customers.

I hope this information is helpful for you.

This GIA article has a tall tale of tanzanite read here https://www.gia.edu/tanzanite-history-lore

I think that zoisite found elsewhere doesn't have the property that it can be heat treated to become blue/purple. I really like the pink/orange 'tanzanite' that is sold as fancy tanzanite. I am also not aware of it being found anywhere other than Tanzania, but I could be wrong.
Prairie zoisite can be found in Wyoming (I have found some)

While gem zoisite and clinozoisite are found elsewhere I don't think they pretty much ever have saturated colors. You can get some grey-purple and even grey-purple-blue from pakistan but it's just not the same. You need that weird low iron geochemistry.