What difference does that make?
Well, lets' see what the dictionary defines as a "citizen" and a "subject".
sub‧ject /n., adj. ˈsʌbdʒɪkt; v. səbˈdʒɛkt/ Pronunciation Key - Show Spelled Pronunciation[n., adj. suhb-jikt; v. suhb-jekt]
–noun
1. a person who is under the dominion or rule of a sovereign.
2. a person who owes allegiance to a government and lives under its protection: four subjects of Sweden.
3. being under dominion, rule, or authority, as of a sovereign, state, or some governing power; owing allegiance or obedience (often fol. by to).
cit‧i‧zen /ˈsɪtəzən, -sən/ Pronunciation Key - Show Spelled Pronunciation[sit-uh-zuhn, -suhn]
–noun
1. a native or naturalized member of a state or nation who owes allegiance to its government and is entitled to its protection (distinguished from alien).
2. an inhabitant of a city or town, esp. one entitled to its privileges or franchises.
Though the differences may seem subtle, I'd say they are quite profound.