Are domain registration, web site, and email hosting all connected?

A friend writes:

I had registered my domain with GoDaddy, with the domain registration (and private registration) paid up through 3/30/2019. Web hosting expires 3/30/2015. My understanding is that the expiration date for the hosting is irrelevant to me now, right? The site and email have been hosted on Gmail for years, so it doesn’t matter that they’re expiring on GoDaddy, right?

And then in 2019, do I just shop around for anybody who charges the least to re-register the domain?

I haven’t uploaded new files to my web site in a while, but I believe the FTP passwords and settings date back to when I signed up with GoDaddy. Do they change?

Confusion on this is common, but easily cleared up:

Domain registration, web site hosting, and email hosting are three distinct and separate services.

GoDaddy is your domain registrar, and also your web site host. Google is your email host.

Of course you want to keep your domain going, presumably forever. And email for @yourdomain.com as well. Whether you continue to want a web site, we can discuss.

Domain: Shopping around for a domain registrar in 2019: I still really like and frequently recommend GoDaddy, who keep their prices pretty low. Namecheap.com is great and the cheapest I’ve found. Hover is just a bit pricier, but the most clean and considered approach. The price difference between any of these is perhaps $7/year, so I don’t choose strictly by price alone. I myself have domains at GoDaddy and Namecheap, and I’m happy with both, but prefer GoDaddy’s customer service, though Hover’s is better.

Email host: Google for Business (using their email et al. with your domain) is no longer free for new subscribers, but you are grandfathered into free. But if you did want to change email hosts, the other one I recommend is Microsoft Office 365 at $5/month or so, depending on the plan you choose. There are others, of course, but those are the two with the most moxy.

Web site: I assume you want to keep your web site live, in which case it’ll be easiest to renew with GoDaddy. (Passwords for your site wouldn’t have changed if you didn’t change ’em; this would be a good opportunity for me to recommend making sure your email and web site admin passwords are strong.) If you did want to change hosts, that’s doable but a longer discussion. If you didn’t want a web site, then just let it expire, but I’d recommend exporting and downloading your content first.