Alan! Good to see you!
Remember, pressure altitude is the altitude above sea level that you would be at on a day when the atmosphere is also standard. That rarely happens.
But... In order to understand the relationship...
We set the altimeter to 29.92 and read it. Let's say today truly is a perfect standard day. The altimeter matches our map and we are at ground level sitting in an airplane on the ramp.
Pressure and temperature are the same everywhere today, and the Earth is a boring place with no weather at all.
The air all around the globe today is a perfect spheroid that matches the planet's shape. A Standard Atmoshphere.
Pressure is (essentially) the weight of the air stacked on top of you. Gravity pulls it down on your head. Heavy isn't it? ;-)
Now today you have a magic knob that you can turn to heat or cool all the air around the planet in one twist instantly.
Turn that knob and heat up that air. What happens?
The air molecules become excited and push each other further apart. The column of air above you has nowhere to go but up. (Let's pretend for a sec, it can't move sideways. We'll get to that in a minute.) All the air around the planet expands upward because it can't go down or sideways.
So it goes up. The column of air above you becomes taller. The spheroid gets bigger instantly.
Here's the kicker: It's weight on your head doesn't change. Still the same amount of air molecules above you as there were before you turned up the temperature knob. Pressure remained the same.
But those molecules are further apart now. When you accelerate a wing (or just walk) through them, there's less of them flowing over the wing (and you) in the same distance, and lower performance results.
That's showing the difference in density.
That's pressure vs density. Raise the air temperature the air molecules get further apart. They don't change their mass/weight.
Think of it like a slinky. The slinky can either be tightly together and held in your hand, or hung from your hand off the ground. It still weighs the same amount.
Pressure measures how heavy the air is above you. Density measures whether or not you can see space between the molecules like between the rings of the hanging slinky.
Now you're saying, in the real world if something magically heated the air above my head, it would move upward, but it would also start flowing outward away from the heated area!
And you're right. That's the key to all weather. Uneven heating of the Earth's surface! Figuring out where that unevenly heated air (and the water vapor it contains) will go, is a whole lifetime of thought, welcome to Meteorology.
Cool, huh? Weight vs space between molecules.