The King as a minor cannot dismiss his regent, because formally speaking he hasn’t been invested in royal authority yet – he is legally speaking a ward of his Regent, who holds that authority in trust. 

So, Regent and Protector of the Realm: not quite the same thing, although they often go together, and they don’t have to happen during a minority. For example, Aemond was Regent when Aegon II was injured, and none of the Regents on the Regency Council of Aegon III were Protectors (not even Unwin Peake). Likewise, Daemon Targaryen was Rhaenyra’s Protector while she was Queen regnant, and Baelor Breakspear was named Protector  by Daeron II.

So how we we understand the meaning of all these royal titles?

Here is how I understand it:

• King of the Andals, the Rhoynar, and the First Men is a recognition that the King is monarch of three nations (in the sense of peoples), both in the sense of glorifying the union of the whole of Westeros but also a promise to respect the customs and folkways of these different peoples. 
• Lord of the Seven Kingdoms is a statement of feudal authority – the king as ultimate liege lord, whose right to rule in part flows from his acclamation and oath-taking by his vassals.
• Protector of the Realm is a military title, recognizing the king as the supreme authority in warmaking – he’s the one who gets to declare war and make peace, he’s the one who calls the banners and who sits atop the chain of command in cases of dispute, and lesser military authorities like the Wardens Cardinal get their authority through him. But as I’ve said before, there’s also a recognition of reciprocal obligation to a social contract: because the King is the warmaking authority, he’s also the one responsible for the defense of the realm against foreign invasion and domestic rebellion.That’s why it’s the King’s Peace and the King’s Justice – he’s the one tasked with maintaining law and order in the face of everything from rebellious vassals to bandits and outlaws to common criminals. 

And this is why I think we see the two titles sometimes separated. Daemon’s Protectorate was a recognition that he was the commander-in-chief of Rhaenrya’s armies; Baelor’s Protectorate was a statement from Daeron II that Baelor was being eased into becoming King, but also a way to counteract the king’s lack of skill by endowing supreme military authority on someone whose martial abilities were unquestionable. Whereas a Regent represents more the civilian side of power – the Small Council and the royal bureaucracy, the judicial and lawmaking sides of Kingship.