Definition & Bedeutung von "[speak] softly (and|but) [carry] a big stick"

What is the origin of the idiom "speak softly carry a big stick" and when to use it?

The idiom "speak softly carry a big stick" is attributed to former U.S. President Theodore Roosevelt and was popularized during his presidency (1901-1909). The full expression is "speak softly and carry a big stick," although it is sometimes shortened to "speak softly but carry a big stick." The phrase embodies a diplomatic approach backed by the strength and willingness to use force if necessary. This idiom is commonly used in discussions related to diplomacy, negotiation, and foreign policy, but can also be applied more generally to situations where a combination of soft speech and underlying strength is advocated.