So a coda is "the concluding passage of a piece or movement, typically forming an addition to the basic structure" (Oxford Languages). A cadence, according to Britannica, is the ending of a phrase.
I've seen some websites define a coda as a sort of "extended cadence", so are they basically the same thing then?
I've seen some websites define a coda as a sort of "extended cadence"
Well, yes. But very 'sort of'. A cadence comes at the end of a musical phrase, a coda comes at the end of the whole piece. And that's about as far as the 'sort of' goes.
Your question suggests that you're just looking at books (or websites :-), you've no actual experience of music that contains cadences and codas. Here's a brief illustration.
Think of a coda as being a part of a piece's formal structure while a cadence is more a part of the harmonic or melodic structure.
For example, take a basic song form — AABA — but now compose some additional material to form a sort of extended ending, or perhaps a musical commentary on the main body of the piece. The form is now AABA+coda. However, each of those sections of the piece could have its own cadence.
The key is Oxford's note that a coda is "an addition to the basic structure." Formally, with a coda, the piece could already have concluded, but the composer chose to add an extension or extra section "after the end", so to speak. Such additional material sometimes serves as an "extended cadence", prolonging what otherwise might be a quick ending.
A cadence typically refers to a smaller structure within the piece, forming moments of pause or separation between phrases or sections.
There can be lots of cadences in a piece, but only one coda. A coda may contain cadences, or it may contain none.
A cadence is a harmonic structure
the end of a phrase in which the melody or harmony creates a sense of resolution.
https://en.wikipedia.org/wiki/Cadence
A coda is an ending part of a whole piece, and it can contain anything rhythmically, melodically and harmonically. Or even complete silence. In pop music it's an "outro".
https://en.wikipedia.org/wiki/Coda_(music)
The Wikipedia page says "Technically, it is an expanded cadence" ... Who writes this stuff. "Technically?" Maybe in old classical pieces, codas usually did something specific regarding harmony.
In music notation, a coda 𝄌 is where you jump to finish off a song. "D.C. al Coda" means, repeat from the beginning, and when you reach the small coda sign, jump to the big coda sign. https://en.wikipedia.org/wiki/Coda_(music)#In_music_notation
"See you at the Coda" is a musicians' saying. Saying "see you at the cadence" would be nonsensical, because there can be cadences all over.
There may be something in the coda section that you could call a cadence, or maybe not.
Codas are like what you get, when you press the Ending button on an arranger keyboard:
That particular coda i.e. ending seems to have lots of cadences programmed into it, but it wouldn't have to have any. It's just a break from the flow of the song, and it probably makes you get the idea that the song is going to end now. It's the opposite of an intro: an intro gets the song started and a coda gets it finished. One could say that a cadence, on the other hand, finishes off a harmonic phrase. But there are other dimensions to musical phrasing besides harmony, of course.
