Welcome to the forum! 
First of all, what you need to understand is that Manjaro is a curated rolling-release distribution. This means that system updates will be bundled together and, after a period of testing via the Manjaro Unstable and Manjaro Testing branches, are then pushed out into Manjaro Stable. This happens on average twice to three times per month, unless there’s an important system component that needs more testing, such as when there’s a major version bump in one of the desktop environments.
Every bundled update also comes with a dedicated announcement thread under the pertinent Announcements category — e.g. Stable Updates for Manjaro Stable, and so on. Each of these update threads details the important changes in the first post, and the potential gotchas — and, importantly, how to work around them! — in the second post. It is therefore imperative, especially if you are a new user, to subscribe for notifications for that category, and to regularly visit the forum.
Updating your system can be done through the pamac GUI, via pamac on the command line, or via pacman on the command line. I recommend using pacman first, because pacman only accesses the Manjaro-specific repositories, and as such you can update your system with the official packages first before updating your AUR packages — more about this below — and your Snaps and FlatPaks.
Manjaro has its own repositories, which contain both Manjaro-built packages and packages that we import directly from Arch upstream. Next to this, Manjaro also offers access — by way of Manjaro’s own pamac or by way of the command yay — to the AUR, the Arch User Repository, which contains build scripts uploaded by Arch users.
It is important to note that these are build scripts, not actual packages — although some of the titles offered on the AUR are binary packages — and that the contents of the AUR are uploaded by Arch users, and thus, for Arch proper, which is a little bit ahead of us on account of its system libraries because we take longer to test everything before it percolates down into Manjaro Stable. But so anyway, the AUR is not managed by Manjaro — and not even by Arch proper — and we take no responsibility for its use.
Next to the above, Manjaro also offers Snaps, FlatPaks and AppImages, all via pamac — again, pacman itself does not access those things. Even though we offer access to those formats, it is again important to note that packages from the official repository bear preference, for lots of different reasons — for one, they take up far less space, and they integrate better with the system.
apt is specific to Debian and Debian-derivative distributions such as Ubuntu, Mint, MX Linux, et al. Manjaro is an Arch-derivative distribution and uses Arch’s pacman or Manjaro’s own pamac. As such, not only does Manjaro not have the apt command, installing .deb packages or .rpm packages is not supported in Manjaro.
Lastly, given the rolling-release nature of Manjaro — and Arch proper — it is imperative that you keep your system updated at all time. Systems that have not been updated, or into which packages are installed without updating the whole system — which leads to a partial update and thus breakage — are not supported.
Normally, you will see an update notifier icon appearing in your desktop environment’s system tray, but as I wrote higher up already, every bundled update always comes with a dedicated announcement thread, and if you subscribe to the Stable Updates category, then you will be notified of such whenever you log on here at the forum — there will be a number with notifications on the picture of your avatar at the top right of the page, and if you click that, you will see the actual notifications.
On occasion, your update notifier icon may signal to you that there are only a few updates. These are commonly urgent bug fixes and security updates to packages that we fast-track for security reasons, such as firefox, chromium, et al.
Finally, the Manjaro Wiki and the Arch Wiki offer very valuable support, as do the member-created tutorials and howtos in the Tutorials section of the forum. Below is one such tutorial — by yours truly — specifically written on account of updating.
