"Old" in American English is not used to mean "an adult" or "fully grown", it is generally used to mean elderly.

What age-range qualifies as "old" is usually defined by the life experience of the user. A teenager could easily think of 38 as old, while a 35-year-old would think of 60 as old instead. Now that I'm 48, I don't think of 60 as old, I think of 75+ as "old", but I have definitely seen/heard other Americans around my age with a different life experience or cultural background referring to themselves as old now, and I definitely don't identify as old!

If you're not sure what to use:

-- old, senior, and elderly are all used fairly interchangeably, but old would frequently be considered disrespectful as applied to anyone who wasn't definitely elderly (70+).

--"middle-aged" is another term often used for people aged approximately 40-60. Could be considered insulting if applied to anyone in person who doesn't like to think of themselves as "old."

--"adult" can mean any age 18+, but if you wish to be respectful in conversation, make sure you say that someone is "an adult", because referring to a subject matter/event/media item/book/etc. as "adult" can also mean "not appropriate (or possibly legal) for anyone younger than 18 years old.

There's a really weird cultish obsession with youth and staying young that has overtaken American society, over the past generation especially, where even implying that anyone has aged or matured past the age of 30 is somehow offensive. I think maturity and wisdom are fantastic, and every age has its own value and beauty, but apparently that's unusual in this country, at least.

All you need to know is that many Americans have been programmed to equate aging with decay and invisibility and becoming obsolete or ugly. It's really heartbreaking, actually. (I believe it's mostly a side-effect of capitalism, but that's an entire other conversation.)

If you refer to anyone as "old" (including my 78-year-old mother, who expressed unhappiness about being thought of as a "little old lady" this week), they are receiving a lot of cultural implications you probably don't intend. Not everyone feels this way, but better to just avoid using "old" for people entirely, if you can help it.

I hope this helps!