My question is: Just because a team scored a bunch of runs, that doesn't mean they'll win, correct? Test is all about strategy and taking the batsmen out, correct?

That's correct. Scoring a high number of runs is a good thing, but it doesn't guarantee that you'll win. You still need to get the other team all out, for less than your total.

This applies for test cricket; in one day cricket, on the other hand, you don't have to get the other team 'all out.' The team chasing the total can run out of balls they can face, in which case they would lose if they didn't beat the total they are chasing. (I'm assuming you're familiar now with the idea that test cricket has 2 innings per team, and one day cricket only has 1 innings per team.)

In terms of strategy in test cricket, think of it like a captain who has to manage 2 important resources: runs and time. His team can keep scoring lots of runs in their two innings, but he still needs to leave adequate time to bowl the other team out twice as well, because test matches go on for a maximum of 5 days. If your team is finding batting really easy, there's no point in batting for 4 and half days, leaving yourself only half a day to bowl the other team out twice. So the captain needs to make decisions on what a suitable number of runs to score are, and ensuring there is enough time to take all the opposition's wickets. The two things are always in balance: the more time you spend scoring runs, the less time you'll have to bowl your opponent out.

Choosing when to stop batting can depend on lots of factors: the quality of the opposition, the conditions of the pitch, the fitness of his team, and also the context of the series. For example, if it's a 3 match series and your team won the first game, and then drew the second, you only need to draw the third match to win the series 1-0. You can afford to be more cautious, amass more runs before deciding to bowl. The other team would be more aggressive, and perhaps declare having scored a low total, in hopes of defending it to ensure a win.

Of course, you might not have a chance to choose when to stop batting at all - the other team can take all 10 of you r wickets and you innings will end there and then, whatever your total. You could get out for 100, and then be in trouble for the rest of the match with such a low score.

Also, regarding this score why does England have a D next to their runs?

This is a good example of such strategy at work. The 'D' means 'Declared.' You'll notice that England were not 'all out.' They voluntarily chose to end their innings having lost only 7 wickets - they "declared" their innings, and decided it was time to bowl.

This was because the English captain Cook decided that his team had scored enough runs, and that the Windies weren't likely to be able to chase the target of 437 in the time remaining - there was no need to score more runs and set an even higher target. If England had chosen to continue to bat, then the captain would have been criticised for being too conservative: every minute longer that they chose to bat meant there was less time left in the game for the English bowlers to get all of the West Indian batsmen out.

As it happened, this proved to be the case: the West Indian batsmen hung on, and managed to draw the game. So some people have criticised Cook anyway, saying he waited too long to declare. Perhaps he could have declared when the lead was only 400. This would have created more time for his bowlers to try and take all 10 of the West Indies' wickets. Or perhaps Cook could have been even more aggressive. What if he had declared with a lead of just 320? There would have been lots of time left in the game. The West Indies might have even tried to chase this total, rather than just blocking to escape with a draw. And then Cook could have been criticised for being too aggressive with his declaration, and throwing away the match by giving the West Indies nearly 2 whole days to chase a small target. It's always a challenge for a captain to figure out the best way to win, and there could be other things outside his control that affect plans, like raining costing time from the match, or players getting injured.

And regarding this game, England did not win because they were not able to get all the Windies batsmen out, correct?

You got it!

If they had taken the last 3 wickets before they ran out if time, then they would have won. There was no way the West Indies were going to be able to chase the target of 437 that they were given, they were just clinging on until time ran out.

But imagine if England declared at a lower total: maybe the West Indies would have tried harder to chase if down, and they would have had more time to do so. Playing more attacking shots would also have meant that the English bowlers would have more opportunities to take wickets too, so the match could have been much closer.

Take a look at this scorecard for another example, and see how close South Africa got before time ran out. And also how close India were to a win as well, needing just 2 more wickets to win. Test cricket at its best.