They are the same thing and both are equally used. Some people might argue that there is a sliiiiight difference in tone, but... I don't really see any difference.

Se pueden usar los 2 pero no son iguales, son parecidos... El color púrpura es como una especie de morado más rojizo... ;)

Nope, "púrpuro" is not possible. It's always "púrpura". Un jersey púrpura, dos cuadros púrpuras.

Both are correct. They are diferent violet tones For example, it is like "light blue" and "indigo"-> Both are blue, and if you call them "blue", everybody will understand you. BTW, there are more violet tones (morado, purpura, violeta, lila, malva, fucsia) You can see here: http://oi60.tinypic.com/2d1l9ow.jpg

Morado/a o purpuro/a... Se puede utilizar cualquiera