there may be nuance on the Chinese side that affect how they translate into English
this one quoted from a comment. yes, there are.
generally, in sequence, the formality is: “璽”, “寶”, “印”, & “章” in chinese; the equivalent in english is: “seal”, “stamp” & “chop”
璽
the official “stamp” of a nation is named “national / state seal” (國璽), like:
National seals of the Republic of China
The National Seal of the Republic of Korea
State Seal of Japan
寶
roughly, the “stamp” used by an emperor is called “寶”. occasionally, the national seal is also called “寶”
the most famous one is “乾隆御覽之寶”
https://www.sothebys.com/en/buy/auction/2022/a-journey-through-chinas-history-the-dr-wou-kiuan-collection/a-highly-important-and-exceptional-imperial
every books, paintings “read” by emperor 乾隆 had this 🙀
these two, “璽” & “寶” are special, most of the time, it was translated as “the seal of . . .”
印
any ”stamp” for authentication (individuals, companies, institutions, officials), is named “印” in chinese.
eg, the seals on calligraphies, paintings would implied that it’s an authenticated products of the owner of the seal.
or, an official stamp (官印), the seal / stamp of any governmental department
most of the time, “印” is translated as “the stamp of . . .” or “the seal of . . .”
章
though “印” & “章” is used together, “章” is less formal than “印”
the most singnificant example is “閒章” (leisure chop / stamp?), which is a “stamp” with lucky verse, proverb, or poem.
this one would be translated as “stamp”, or “chop”
last, there’s a specified character “鈐” (u+9210), used as a verb, which means “to transfer pigments onto a surface using a stamp”
last, if you can read literary chinese, and have access to internet archive, there’re books talked about sigillography (“印學”) 😸
have fun :)