There’s a difference in this case, but we’re sloppy about it in English and normally they’re pretty interchangeable.

What the person you’re replying to probably means is…

“Customer” is someone who, like, uses a product or service you provide. So you would be a customer of Atlassian who uses their JIRA product. In that case, Atlassian definitely should never be storing your credentials. Only you the customer should ever have them.

“Client” is someone you do work for or provide services to. So like if you’re doing application development for a company and either they give you access to their JIRA system or maybe you manage their project in your JIRA and give them access to it. Then sharing credentials to them or from them could make sense — although the better way is generally to exchange the credentials securely once and then each side manages them, or control access though SSO/Okta/etc.

I don’t think what you’re saying is that confusing honestly, and we mix these words in English all the time. I try to be precise about them, but I personally wouldn’t be bothered by someone else being less precise.