That said, dialogue gets odd. Let me put that into perspective:
Sammy looked at Jimmy and sighed, "The radiologist did not use the term 'herniated disc'. He did, however, describe one!"
So if it's dialogue and being quoted, it goes in single quotes, because the dialogue itself goes in double quotes.
To be more general - what Step is describing is a nested quote. When dialogue is quoting, the inner quote gets the single quote where the dialogue is in double quotes, but where the dialogue is in single quotes, the nested quote (the inner bit being quoted) gets double quote marks.
It alternates. Whichever is the convention (and in some cases, it's a matter of personal preference of the writer), the first nested quote gets the opposite. But if, heaven forbid, there is a nest quote inside the nested quote, then it goes back to the double quote.
I'll try and demonstrate (warning - it gets complicated) -
Jack called Jenny over. "Jenny, when I said, 'Jump!', I meant you to really leap high."
Jenny replied, "Thanks for clarifying. By the way, Peter said to say to you, 'Will you ask Jack if he told the teacher, "Get lost!"? Because I heard that Jack got suspended.' So, Jack, did you? Get suspended, I mean."
Technically, that is how you do it. But in practical terms, it can get too complicated for a reader to bother with trying to keep track. And when you lose your readers, it doesn't matter if you are being grammatically correct.
Also take note of where I put the exclamation marks and the question marks.
On the spelling of disc/disk - in Australia, computers have disks. Everything else is a disc. The reason - Australian English/UK English convention spells it as "disc". But US conventional spelling of "disk" is used in computing, because a lot of computer-related production and marketing has come out of Silicon Valley, and the US convention tends to stand in computing terminology.
Other changes in UK/Aussie English are happening - "program" is a US spelling originally. It especially related to computer programming, but increasingly in Australia we talk about TV "programs" and not "programmes" which is how it was spelt when I was in school. For years I insisted on "programme" but I realise increasingly this is chauvinistic. I'm learning to give in. A lot of other "-amme" words have gone the same way, been shortened to the US spelling (saves ink and paper).
C'est la vie...
Marg
When I was a kid, the Aussie convention was for dialogue to be in double quotes. But increasingly lately, I'm being asked to use single quotes. I prefer double, but I will follow the convention my writer insists on, especially where that writer has academic experience and strong preference. There is a lot more flexibility these days; conventions change, rules change.