Ciao!
well, "vorrei" and "voglio" are both conjugation of the verb "volere". The difference is:
-"vorrei": is the Conditional tense. Examples are: " Vorrei una coca cola, per piacere", "Vorrei andare in vacanza ma non ho abbastanza soldi" In English it´d be "I´d like a coke, please", " I would like to go to vacation, but I don´t have money enough". At the beginners level "vorrei" is used to ask something politely in a bar, restaurant,shops etc.
-"voglio": is the present tense of volere. Examples are: "voglio andare al cinema", "voglio quel vestito". In English it´d be "I want to go to the cinema", "I want that dress"
Hope it helped, if you have further questions just write me :o)