Murder is the intentional killing of another. But it's not always so simple. The thing with murder and manslaughter is that there are multiple degrees and different types of killing.
The basic definition of murder is the unlawful killing of another with what lawyers call "malice aforethought." That term refers to the level of intent, which requires some degree of premeditation. By that, it doesn't necessarily mean that the murder was planned out. It just means that the murder was deliberate, or the product of a certain degree of recklessness.
At the highest level, a first degree murder charge is as bad as it gets. It's typically a murder with the highest level of intent and possibly other unfavorable circumstances.
Here's a look at first degree murder in New York: