It depends on the monitor and the resolution, but for a typical monitor and a 1080p resolution you can tell that there is a difference.
You can see a difference on most of the 4k displays I've tested (Samsung, LG, Acer, etc) but not on most 1080p monitors.
The difference is most noticeable when you're looking at a single pixel on a page or a black image.
If you have a 4k monitor, you may see the difference when viewing large images (like the ones you see in the picture). But you can't really tell the difference in the picture on the screen itself.
To answer your question, yes you can tell the difference between 4k and 1080p on a monitor, but you can't really see the difference.
Yes.
You can tell the difference if you are looking at a photo.
4K is higher resolution and 1080p is lower resolution.
In a few years time, I'd say the difference will be so negligible that it will be completely irrelevant. But for now, yes you can. If you have a 4K monitor, you'll notice the difference in the higher resolution display.