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Quick Jump makes High Jump and Long Jump single actions.
Powerful Leap adds 5 feet to your Leap distance horizontally.
Do these work together? One of them talks about Leaps, the other Long Jumps, are these the same thing?
So if I have both with a Speed of 25, can I use a single action to Leap 15 feet without a check, and with an Athletics check DC (Distance-5)?
Leap is a 1-action jump that does not require a check.
You take a careful, short jump. You can Leap up to 10 feet horizontally if your Speed is at least 15 feet, or up to 15 feet horizontally if your Speed is at least 30 feet. You land in the space where your Leap ends (meaning you can typically clear a 5-foot gap, or a 10-foot gap if your Speed is 30 feet or more). [...]
Long/High Jump are 2-action activities that require an Athletics check to measure success.
You Stride, then make a horizontal Leap and attempt an Athletics check to increase the length of your jump.[...]
You Stride, then make a vertical Leap and attempt a DC 30 Athletics check to increase the height of your jump.[...]
Notably, Leap is part of the Long and High jump activities, so you do gain the Powerful Leap benefits for those, and Quick Jump reduces them to 1 action. However, there is still a regular Leap action available to you (although as @BenBarden correctly points out, Quick Jump means that you would only use Leap if you were concerned about rolling a critical failure on the Athletics check).
From Long Jump:
You Stride, then make a horizontal Leap [...]
Note that "Leap" uses a capital letter so it is used as a standardized game action and not as some casual english word.
So thanks to Quick Jump, you use 1 action to Long Jump. Long Jump makes you Leap. And finally thanks to Powerful Leap, you can add 5 feet to the distance your Leap would ordinarily cover.
Also "Powerful Leap" has an impact on any Leap you make, even if you do not use the Long Jump action to Leap (e.g. as Ifusaso stated in their answer, when you use the Leap basic action).
