Yes they use different repositories and release models. Leap uses a normal versioned release model (like Ubuntu for example) where packages are in a "stable" state and only non-breaking patches and minor updates are available for that release. Tumbleweed is "rolling", which is explained here https://en.opensuse.org/SDB:Upgrade_Tumbleweed. With Tumbleweed you are expected to manually update to new snapshots using zypper dup, and it is a bit more work to manage especially for new Linux users. it is also recommended to disable GNOME and KDE's automatic updates, since individually updating packages reduces the benefit of the openQA quality checks for Tumbleweed which depend on snapshots (which appear as new distro versions to zypper). I personally uninstall Gnome Software completely, and I like to use zypper -vvv dup --no-recommends as recommended packages can sometimes add unnecessary bloat to the system.
openSUSE
openSUSE is an open, free and secure operating system for PC, laptops, servers and ARM devices. Managing your emails, browsing the web, watching online streams, playing games, serving websites or doing office work never felt this empowering. And best part? It's not only backed by one of the leaders in open source industry, but also driven by lively community.
What is the operating system though? Is it just a few core packages or is it pretty much everything that I included on the install? I’m just not sure what’s updated regularly as opposed to what’s released with the OS update.
I think this will make more sense if you understand how repositories work. You can take a look at this link for the openSUSE repositories, and can Google for the basics on how a repo works if needed https://en.opensuse.org/Package_repositories. As you can see there is only ONE repo for tumbleweed, and there will always only be one, as it always contains the latest versions of packages accepted into Factory. However, there are multiple Leap Repos containing curated combinations of package versions that create a stable system. In theory, everything you install from the official Leap Repos should just work within that version of Leap. However in order to get this kind of stability Leap does not always package the newest version of every software in a given Leap release. Sometimes newer is not better, as adding new features can uncover bugs upstream and downstream, which may not always be fixed in time for a Leap release. With Tumbleweed, you get the double edge sword of being the first to possibly see any bugs, but also be the first to see the bug fixes.
As to whether or not certain packages are included in the Leap repos, both Leap and Tumbleweed are curated in what packages they contain in their core install.
For Leap, if you need a certain package it may be critical to check in the core Leap Repo whether it is included, because installing the latest version of the package from a 3rd party repo may not go well with Leap's older versions of upstream software.
For Tumbleweed, I've found that the newest versions of most 3rd party Linux software rarely encounter any issues with the upstream packages included in Tumbleweed. This makes sense, as new versions of downstream software might be expected to utilize newer versions of upstream software. But again, while openQA makes Tumbleweed the most stable rolling distro, you will see bugs and you should have the knowledge to know how to deal with rolling back packages (or your whole system) if things don't go well.