It’s nearly meaningless to just quote DPI numbers as a measure of the quality of printing unless you add some context such as halftone frequency.
A 2400 dpi imagesetter can indeed draw 2400x2400 black or white dots in a given square inch, all individually addressable. This means you can produce a 2400 dpi black and white image with no levels of gray. This is not very useful, but I’ve done it.
Now instead of just having 2400 dots per inch, imagine that you divide this 2400x2400 into little 2x2 cells of dots. There are 1200 of these cells per inch, and each cell has four dots that can either be on or off, meaning the cell can be all white, all black, or a few shades in between (1 of the 4 dots black, 2 of the 4, or 3 of the 4). This makes your 2400dpi printer into a 1200dpi printer if you only need 5 different levels of gray (0, 25, 50, 75 and 100%).
Now imagine that the 2400dpi is divided into larger cells of 8x8. Now each cell has 257 different levels of gray it can display, but you only have 300 of these cells per inch. This is what it means to say that usually, even commercial printing has an effective resolution of 300dpi. Each color plane (cyan, magenta, yellow and black) is technically 2400 dpi, but it’s divided up into little cells in order to give better control of color levels, so there are really only 300 individually settable “pixels” of color per inch. This is a process called halftoning.
Interestingly, even though there are higher resolution imagesetters than 2400dpi (as the 4800dpi mentioned), halftone dots still tend to get printed at around 300 per inch (“lines per inch” in halftone terminology), because in traditional offset printing, there are limits to how small and close together you can make ink dots without them losing their shape and/or running together on the paper.
But the bottom line is that if you printed your 7000x7000 JPEG on a business card using a 4800dpi imagesetter, it would look like garbage, either because it would be downsampled to 300dpi and halftoned, or because it would be printed at 4800dpi but with 1-bit color fidelity.