Hello Jessica,
additional to Anelise's answer, some examples and a further hint:
"wollen" is stronger than "wünschen", you use the word "wünschen" for example if you are not sure of the occurence.
"Ja, ganz sicher, ich will ein Pferd."
("Yes, for sure, I want to have a horse.")
"Wir wollen eine Wohnung kaufen (und sind auf der Suche)."
("We want to buy a flat (and are already looking for one).")
"Ich wünsche mir einmal nach Dubai zu fliegen".
("I wish to fly to Dubai once.")
"Ich wünsche mir, dass ihr anständig seid" ("I want you to be honest" -> parents can't be sure if their children follow the rules ;) )
Hope this helps...
Matthias