It’s weird but the amount of natural numbers is “countable” if you had infinite time and patience, you could count “1,2,3…” to infinity. It is the countable infinity.

The amount of numbers between 1 and 2 is not countable. No matter what strategies you use, there will always be numbers that you miss. It’s like counting the numbers of points in a line, you can always find more even at infinity. It is the uncountable infinity.

I greatly recommand you the hilbert’s infinite hotel problem, you can find videos about it on youtube, it covers this question.