So I'm running into trouble already over something I'm sure is simple.
Google Domain registration promises 100 email aliases, like
blank@mydomain.com. Well HostGator says that I have to change the nameservers on that domain from Google's defaults to their own. The moment I make that change, though, Google says that the 100 email aliases service is no longer available, and that if I want it, I have to keep the default nameservers. But if I want to use HostGator as my webhost to actually build a website, I need to use their nameservers, right? So basically Google Domains isn't doing anything for me? I don't understand this at all. Am I supposed to set up my email accounts through Google Domain or through HostGator? Does that fall under a domain or a webhost issue?
Your earlier analogy was pretty accurate.
As such, you have to remember that Google Domains is serving primarily as your domain name registrar. That basically means that the primary thing you should expect from them is just a place to register your domain name. Any other services they offer above and beyond that is them bleeding into what your hosting provider (i.e. HostGator in your case) offers you.
This includes hosting
and email services. As you already noted, what Google Domains offers are free email aliases, which is basically a way to forward emails sent to
whatever@yourdomain.com to a Gmail address of your choice. This is an easy way to be able to have any custom email address you want, and it just goes straight to whatever Gmail address you might be used to using. It does not actually function as a real email account that has it's own inbox and ability to send emails. It just passes things along to the Gmail address you chose.
Google Domains does offer some hosting services as an addition to your existing Domains account. They cost extra per month, and go through some third parties like Squarespace & Weebly, and you'll find them in the "Website" section of your domain's management page.
However, if you decide to use a separate hosting provider (i.e. HostGator), then you'll have to give them the information they need to forward your domain requests to their hosting. At this point, it might be helpful to have a better understanding of how these things relate. I'll try and give you the basic gist of it.
As you may or may not know, every device on the internet is identified by an IP address, typically of the form ###.###.###.### (e.g. 173.194.115.2). No one in their right mind wants to type that in, instead of "google.com" though, so that's where domains come in. You need some way, some
directory, to be able to translate any user's request for "google.com" and send them over to "173.194.115.2". This is what DNS (Domain Name System) is for, and that's what nameservers do. They point the domain you purchased to the right address.
So, at this point, Google Domains defaults to pointing to its own nameservers. This is fine if you're going to use their hosting services (including the email alias/forwarding service). However, in this case, it seems you want to host your site on HostGator, so you'll have to provide them with the correct HostGator nameserver. So that way when people go to "yourdomain.com", they will get directed to HostGator, and then the HostGator nameserver will go "oh hey, that domain is in this particular location in our network at this ###.###.###.### address".
The end result is, if you want to use Google's hosting/email services, you keep things as is. If you want to use HostGator's services, you change the nameserver for your domain. You can't have both. Not unless you roll your own anyway, and that's a whole lot more complicated than I'm willing to go over before I go to bed.
I've never used HostGator, but if they're not horrible, they should have some form of customer support. Don't be afraid to ask dumb questions. You're paying them for a service. Don't worry, it's not as hard as it seems, but it's also typical to bump into tons of little problems you have to work out. You're doing fine. Good luck.
