No. Nightmares and night terrors are different sleep events that occur at different stages of sleep. Nightmares are bad dreams you usually wake from and can remember; they tend to happen later in the night. Night terrors (also called sleep terrors) happen while a person is still asleep—often early in the night—and may involve screaming, thrashing, or moving about, with little or no memory of the episode afterward.
The NHS notes that night terrors are most common in children ages 3 to 8, while nightmares can affect both children and adults. Sleep paralysis is a separate condition and is not the same as a night terror.