Seriously, don't risk embarrassing your boss. If it's that big a deal to you, quit, and find a job somewhere else with a better boss.
As the old saying goes "What an interesting game. The only winning move is not to play".
1) Don't let your boss know, because it could threaten your job.
2) If it's that big of a deal to you, quit and find a new job.
If you really can't get over the fact that your boss is using terms incorrectly, send them a polite email. If you're not on close terms, just get over it.
Edit: I should perhaps have been more explicit in saying that I meant "start looking for a new job so you can quit" as opposed to "rage quit on the spot".
Me: "Wait, hold on, when we are talking about Agile, do you mean Scrum? Like the one with weekly sprints?"
Boss: "What's a sprint? I mean those guys who handle the AWS and servers and backups."
Me: "Ohh, so you meant DevOps?"
Boss: "Yeah, that's the word."
Me: "Ohh... I used to confuse those words a lot too."
Just be polite, don't make them feel embarrassed. Take a neutral tone. Do it for clarification, not because it hurts your ears.
A few years ago I had a manager that would claim that we did BDD all the time because we wrote user stories. We did no unit testing of any kind, and it put us in hot water with a potential client when they asked to see our BDD framework. I had tried to tell him on a number of occasions that there was more to BDD than writing user stories, but he never stopped, and it made the company look a bit silly. It wasn't a personal thing as we got on really well, and he relied on me a lot for support, so not sure why he didn't take the correction on board.
All you can do is privately tell them that the term is incorrect. If they continue to use them incorrectly then that's their problem.
I once corrected my manager when I was contracting at an Australian ISP. It was something about browser cookies I think. As soon as I told him he's wrong, (we were in a pretty open-plan albeit half empty office) he just stopped talking, turned his chair around and went back to work.
I asked him if he had things for me to do for 3 days always with responses of just "no", before I contacted by contract manager (affectionately referred to as "pimps" in Australian contracting) and explained the situation.
Later that day the manager turns to me and says I did the wrong thing by talking to my pimp - I should have talked to him directly instead. The irony was lost on him I think.
Anyway. I'd still do the same thing in that situation (technical discussion that affects work).
But if a guy who doesn't actually do the technical work insists on saying "depreciated" instead of "deprecated" or "jdk" instead of jvm, but others know what he meant, it's probably harmless.
It turns out in tech people use the same jargon in different ways. If I'm able to understand what they are saying, that is the important part and I just move on. If I'm not quite sure how to interpret what they are saying, I'll try to clarify.
If its a pretty glaring mistake, and you really feel the need to correct the mistake, muzani's script is pretty good. You could even go with "Oh, I've heard that called xyz before."
If someone wants to replace the word DevOps with Agile, I say why not. At the end of the day the bits and bytes don't give a damn what they are called.
I dunno... they are back to killing the Boss about every other episode or so here lately, from what I can remember. Or maybe it was Consultants they were killing off. Or Salespeople...
If they are miscommunicating, you can always ask them what they mean when they use the term, and say it's because you want to make sure you understand what they are saying, and you've heard the term used in a different context and want to make sure you and they are on the same page.
Try asking clarifying questions to push your manager to expand their understanding. Some ideas are:
"What do you mean by X in that context?"
"Thats interesting, how does that work exactly?"
"I've heard of x used as y, how would it be used in your example?"
Go rogue and publish a glossary of techncial terms with public references and post it up in your office.
Clarity is key. If your manager is using terms incorrectly, they are likely confusing others on the team or representing the team inconsistently. In the end they need to get their skills up, get more info, or get out of the way. IMHO.
If you are close with your manager, have a chat with him/her in private and let them know politely what the correct terms are without offending them. If you're sincere and genuinely concerned about your boss, he/she will be thankful. The tone and intent of delivery counts.
If you're just looking to correct him/her because you feel you are smarter/better than him/her, it would be better not to. Not everyone is perfect.
Proceed with steps beyond #1 only when you have enough trust and rapport. Never correct in public.
You could take solace from Dilbert. every workplace seems to have one or more PHBs.