A good example would be when playing an easy game, and you tell a player that you're expecting a win. The match isn't an 'important match', but they will feel very pressured by the team talk, and if they can handle the pressure, it will motivate them, but if they can't they might become overcome with nerves.
That's about how I understand it. Pressure dictates how you handle the day-to-day pressures of being a footballer: manager team talks, press conferences, media attention, comments by opposing managers, keeping your cool during an extended title run, etc.
Important matches, however, not only indicates how well you cope with the pressure of the big matches, but how easy it is to motivate you for those matches.
So a player with very high Pressure-handling may not get nervous, but he may not necessarily be very easy to motivate either whereas a player who loves important matches will, more often than not, get motivated for the big games.
To visualize this, a generally neutral player will have a motivation spectrum that looks like this:
Can somebody clarify what would constitute an important match? Derbies, semi-finals, and finals are the obvious ones, but anything else? Shouldn't every league game be an important match unless the team is already won it early?
Any cup match against opponents of high reputation. When my non-league side gets drawn against league opponents in the FA Cup it's an Important Match. I tell them to go out and enjoy the experience and they do pretty well.