I'll be extra clear by showing 2 different ways to think of it.
If you were to already spin a "16", for example, and you ask, "What are the odds of hitting 16 on the very next spin?", then the odds are exactly the same as they always are: 37 to 1. (1 out of 38 is the chance.)
That's the same for ANY number that has just come up. Most likely, this is the answer you were looking for. You walk up to a roulette table, you see a number has been spun, and you're wondering what the odds are of hitting that same number. It's ALWAYS 37 to 1 against that number repeating. No more and no less.
HOWEVER, if instead you walked up to a table and were wondering, "In these next 2 spins in a row, what are the odds of hitting specifically the number "16" on BOTH spins?", that would be different.
The odds against you hitting 2 specific numbers 2 times in a row are 1,443 to 1 against you. (1 out of 1,444 is the chance.)
Again, this is the same for ANY number. Not just 16, of course.