somebody on the comment section mentions that the term means the same thing in medicine as it does in everyday speech (which means strikingly different from its surrounding)
Yes, this is the meaning of "contrast": something strikingly different from its surroundings.
In the context of images, we would say a black and white image has high contrast: there is a striking color difference between black and white. An image with two shades of grey would have less contrast, because there is less of a color difference between shades of grey than between black and white.
MRI works by using a magnet to polarize the spin of nuclei, and then letting things "relax" back to baseline. But we don't just use MRI to spin things for fun, we use MRI to make images that are useful for diagnosis and research. That "relaxation" occurs at different rates, which is what is used to differentiate (contrast between) different tissues. T1 and T2 refer to different types of relaxation. When someone says "T1 contrast" they mean "using an MRI to generate an image where the difference between black and white (contrast) indicates different T1 relaxation". Same thing for T2.
Also I hear about "contrast" on/of X ray film
X-ray imaging works by projecting x-rays through some tissue onto film. Some things, like bone, don't let x-rays through as easily, so this creates contrast on the film: places on the film where a lot of x-rays hit and places where fewer x-rays hit.
This works decently well with bone because bone blocks x-rays by itself, but for imaging other tissues like the digestive tract or the vasculature, one might use a radiocontrast agent. These usually contain iodine or barium, heavy atoms that block x-rays. It'll be in a solution that you drink to image the digestive tract or is injected into an artery/vein to image the vasculature. Sometimes someone might say "contrast" as shorthand for "radiocontrast agent" or equivalently "a substance that will increase contrast in an x-ray image".
So, in summary, yes, "contrast" is just describing things that stand out against a background. In medical imaging, images are created. The word "contrast" can refer to differences that are visible in those images, or the methods used to create those differences. The specific meaning depends on the context and the type of imaging.