It is only a partial upgrade if you update your databases, without upgrading the rest of your system. If you try to pacman -S firefox, and it gives you a 404, you have to both update your pacman databases, and upgrade your packages. This will only give you a 404 if you cleaned your package cache, and your package is out of date. Usually, -S on an already installed package will reinstall it from cache. This does not cause a partial upgrade.

If you run pacman -Sy, everything you install is now considered a partial upgrade, and will break if you don't know exactly what you're doing. In order to avoid a partial upgrade, you should never update databases (-Sy) without upgrading packages (-Su). This is usually combined in pacman -Syu.