Applications don't transfer into correct resolutions?

I have two monitors, one that's 4k and one that's 1920x1080. Some apps open in 4k resolution and some open in 1920x1080. When I try to move an app from one screen to the other, they appear fuzzy or they just barely work. For example, I tried playing minecraft. It works well on the 4k screen but when I move it to the 1920x1080 screen (The screen I want to play it on) it isn't in the correct resolution and it appears fuzzy. So, you know when you have a window not fully maximized and it shows the borders on the top, sides, and bottom, well minecraft has the borders on the left when maximized. So it's obviously not maximized. And since it has that border on the side, minecraft doesn't play well and what not.

Most programs are written for some ideal resolution, or for many resolutions but have no ability to swap to another if you drag the open game or application to a different monitor, video driver and resolution setting.
Change which screen is the primary, which is the extension in display settings. THEN open the program and it will appear in that primary screen either as full screen, or if you chose, in windowed mode.
That is all that can be guessed from no details on what operating system in what PC, what other programs besides "minecraft" you might run.
An alternative is use only matching resolutions in the two monitors.