Just to expand on the previous answer.
Is my reasoning correct, a wordlist is only useful if there's words in the password, and wastes time if there's not?
It's not necessary for the password in question to contain words. It depends on the wordlist itself. A good wordlist can save you a lot of time. Some popular wordlists not only contain words that one would find in a dictionary, but also a few mangled words (I'll get to this in a bit). Programs like john and crunch can help you create a custom wordlist for your target. But yes, It is highly unlikely to find a randomly generated password in a wordlist and atleast some part of the password should contain words to improve your chances of a wordlist based attack.
I know in John the Ripper there's word mangling rules, what is this?
Now, this is an interesting topic. Word Mangling (in case of johntheripper) is in simple terms mutating all the words in a wordlist according to rules defined in /etc/john/john.conf (on a linux machine). I'll explain this better by example.
Users most commonly tend to mutate their passwords in various ways. This could include adding a few numbers at the end of the password, swapping out lowercase for capital letters, changing certain letters to numbers, etc. So lets assume that you know a particular person (or victim in our case) likes to append two numbers at the end of his/her passwords (which in most cases is a word to remember it better). You can add a rule in johntheripper's configuration file.
And after that you create a mutated wordlist with the following command.
john --rules --wordlist=/path/to/wordlist --stdout > new_word_list
This will create a new wordlist (using the rules in the config file) which is a mangled version of the old wordlist, which will better your chances of a successful wordlist attack. Similarly you can append stuff (characters, numerals, special characters), change characters to upper/lower case, change specific indices to a character of your choice, etc just by adding the relevant rules to the config file. I'm not sure how to explain this better, but i hope you got the gist of it.
By the way, are the terms "dictionary" and "wordlist" usually used interchangeably in this context?
Yes, in this context "dictionary" and "wordlist" are interchangeable terms. This is because when the attack first came out, hackers were literally using words from the dictionary as a wordlist (people back then didn't use strong passwords). As people became aware of the "dictionary-attack", they started mangling their passwords (eg, horses1234, alabama12, etc). So the hackers developed their methods and came out with a mangled version of the dictionary. And (over the years) after all that mangling, adding slang, etc the resulting wordlist looked nothing like a dictionary and hence hackers started referring to it as a wordlist.