Should I use pt or px?

Yes, "px" means "pixel"

Now that I said it, I can already hear an army of clairvoyants approaching, with "px has nothing to do with pixels" on their banners. They're so proud of knowing better that they look up every comment containing the original truth and explain in detail that it's false, incorrect, misleading, etc.

And yes they have a point - a very specific point in time, actually, called iPhone 4.
Here's what happened.

The peaceful days

Before Retina displays, one pixel was one pixel. Because that's how it should be, according to human logic. You put a single pixel line on the screen, you magnify the hell out of it, and there you go: it's exactly ONE PIXEL wide. On many hardwares, modern ones included, this is still the case, so it's everything but "incorrect" to say 1px = 1 pixel.

But.

Back then, one day, iPhone 3 was followed by iPhone 4, doubling the resolution in both X and Y, and the developers of Safari worried that all webpages will look ricidulous, especially because many web developers relied on the steady 320x480 resolution. So just creating a 640x960 pixel area would have killed most of the sites. And at this point, someone had the billion-dollar idea to introduce a magical beast: a CSS feature called -webkit-min-device-pixel-ratio - on iPhone 3 it was 1, and on iPhone 4 it was set to 2 by default. Meaning "1 CSS pixel now means 2 screen pixels". A very ugly hack to keep websites look somewhat intact - it worked at that time, with the very small cost of some images looking a bit blurry, but in the long run it caused this worldwide misunderstanding of poor old px who actually did nothing wrong.

So then: pt or px?

On screens, use px because on many-many displays it will mean ONE PIXEL. The biggest advantage of using pixels is they look crispy; even if 1px means 2 or 3 physical picture elements, whatever you draw will start at the boundary, not somewhere-in-between. This is very important. Watch any browser animation that includes text, especially size transitions: when you increase a div to double size, but slowly. You'll see how your browser recalculates its pixels and redraws the font when the animation is done. There's a temporary image of the area which is a little blurry - to make the animation itself smoother -, and then, after reaching its final state, a more exact image is calculated. See this CodePen.

1px is always an integer multiplication of hardware pixels; that is, unless your operating system is being smart like resizing your whole desktop to sqrt(2) x PI. Or just 125%, yes, hello Windows on tiny laptops. But anyway - with px, you have the highest chance to align your things with the physical grid.

What about pt? The funny thing about pt is it's actually translated to px, so it's just a worse way to specify pixel sizes. Here's a calculator. Points (since they come from the print world) start to make sense when you print something, but today there are better alternatives, depending on what you need - so tbh, points are almost never needed.

TL;DR

For screens, use px whenever possible.