Would the US Declaration of Independence be improved if it said "life, liberty and the pursuit of hedonism"?
Do you think they ran this competition so we all realised that our happiness is not based on possessions? Or is this a side-bonus?
Probably they just didn't think it through. On the giveaway page itself, first they say:
All sorts of things make us happy, from the home we live in to the whisk that beats the eggs for our morning omelette. We are seeking to discover what you buy that delivers the most happiness.
Then after that:
All you have to do is take our brief survey telling us in which purchase over the past 10 years has given you the most pleasure, and why.
The fact that they used 'pleasure' there tells me they aren't actually considering the difference between the two.
Are they always different?
It's a matter of scale. Happiness is something you measure on a longer timescale than pleasure. Drinking beer can give you pleasure but not happiness*. A puppy that just shat on the rug doesn't give you pleasure, but the puppy does lead to more happiness. I assume. I recall some studies saying that pets are good for your mental health and life expectancy, but if you ask people about their happiness, they might not take into account their mental health and life expectancy.
Self-report measures of happiness support the idea of the 'hedonic treadmill', which says that you can have good or bad events in your life but these do not have an effect on your overall happiness in the long term. Usually, buying a new house or losing a close family member strongly affects your mood for some time, but before long you'll have adapted to the new baseline, and you don't feel more or less happy than before. That's also why money can't buy happiness: Beyond the minimum standard of living, more money may give you more pleasure but it doesn't affect your long-term happiness. Without that minimum standard of living, the day-to-day struggle to get by puts such a significant damper on your mood that you just can't reach a comfortable state that people call 'happy'. That goes for other things too, and as Valdís indicates, resolving gender dysphoria gets rid of that damper and really makes her more happy. So unless there's something that actively makes your life worse every day, most people would consider themselves roughly equally happy all the time. That's basically my whole view of happiness.
*I know, "only if you stop drinking."