DnD 5e, forced movement


So, movement speed is apparently per round, not per turn. So let’s say character A walks 30 feet, their full movement speed, during their turn. Then character B casts a spell which forces character A to move another 30 feet due to fear. What happens? Isn’t character A’s movement speed already used up? And what happens in reverse, if character A forced to use their 30 feet at the start of the round due to character B’s spell, can they move 30 feet on their turn?

References to the PHB would be really appreciated in any answers, and thank you so much for the help!