Wrong power adapter for laptop?

Since my adapter for my laptop has now given up the ghost, I plan to buy a new one but am a little confused by this sentence.

"Only use with power supply unit blablabla"

And now my question. It doesn't really matter what kind of power supply it is, as long as the output from the power supply is correct, right?

The power supply unit must have 19 V, at least 3.42 A and the size and polarity of the plug must match.