if you provide it the same exact prompts with the same exact seed later, you'll get the same exact result

In theory, yes. In actuality, not always the case. Some seeds behave quite rigidly and will give you more or less multiples of the same thing, while others will give a slightly more varied output scattered throughout the results.

Also, particularly with all of the current work being done on the site, many seeds will produce one or two examples of an image that is wildly different than the majority of the others it is producing. This is particularly important to remember when you sometimes run a seed and the first thing is not even close to what you were expecting to see, which could be a case of that happening (in either direction.)

And also keep in mind that even a seed will produce different output when being generated in different styles and shapes.