Is "purchased" more formal than "bought?"

Is "purchased" more formal than "bought?"

It was suggested to me that the correct verb to use referring to something
I paid for in the past is the word purchased:
I purchased x.
instead of
I bought x.
As far as I can tell, the words are almost the same in this context. The
only thing I've seen online is that boughten is a colloquial past tense of
the word bought.
Is bought ever, if rarely, considered colloquial? Is it ever improper to
use when referring to a recent purchase?