This month, Loki has wrapped up with a finale seeing Loki becoming the new He Who Remains. During the second season, the show has expanded on the multiverse, a concept already established in Avengers: Endgame, Loki season 1, Doctor Strange in the Multiverse of Madness and Ant-Man and the Wasp: Quantumania. However, the multiverse comes with a lot of rules and mechanics, and even a bit of mythology. The MCU thus plays more soft with it's rules and becomes more science-fantasy (1).
In Avengers: Endgame, Bruce Banner establishes one fundamental rule for timetravel: everything that has happened is the past, and that past can't be changed. Even if the traveler is from the future, that future then becomes their past. Thus, if one is to jump (or slip) to another place on the timeline, a branch is created which continues to exist next to the original timeline. So, no timeloops. Even the Sacred Timeline itself could be a branch, as it is influenced to prevent another Multiversal War (including contingencies like Victor Timely in 1893) by He Who Remains, a timetraveler from the 31st century.
The Many Worlds
Branches can also be created through superpositions. A famous example of this is Schrodinger's Cat. In short, the box the cat is in is a quantum system (a closed system) and the superposition is the cat being in two states: alive and death. Upon opening the box, an observation is made and the system collapses into one state. In the Many Worlds Interpretation of quantum mechanics, the universe makes a metaphysical split: one where the cat is alive, the other dead. Or in case of Quantumania's probability storm, they happen concurrently as time and space are irrelevant in the Quantum Realm.
An example of quantum system collapse leading to branches, are variants like Sylvie and Loki. In this quantum system, the two states are the Jotun being born female or male. In the Sacred Timeline the Jotun becomes the male Loki, but in another the female Sylvie (which kind of makes them siblings, as they share the same parents). And that is allowed up to a point by HWR's vision for the Sacret Timeline. Only when a Nexus Event is reached, that universe gets pruned. For Sylvie that was playing with toy dragons. Or maybe even a choice, as consciousness can also be seen as a quantum system (do I go left, or right?).
Realities: timelines, universes & dimensions
Aside from branching timelines -that get created as a result of timetravel or quantum systems collapsing into different states- there are also parallel universes. These are not branches of the Sacred Timeline, but instead follow seperate timelines. However, they do operate on the same rules of physics, like gravity, entropy and thermodynamics. Thus it's a seperate reality, but not with seperate rules. Examples of such universes are the Raimi & Webb Spider-Man movies or the 838 universe seen in Multiverse of Madness.
A consequence of universes interfering leads to incursions. There is no explanation as of yet why that is, but it could be that for the law of preservation of energy is broken, resulting in all out destruction. Dimensions, such as the TVA, the Quantum Realm, or Ta-Lo, don't appear to suffer from this, but that could be because they are outside of spacetime (the three dimensions of space and the one of time that make up the universe) and follow different rules of physics. These places do share similarities though, as both Ant-Man and Victor Timely spaghettify in identical ways in the Quantum Realm and the TVA.
Science/fiction
However, not everything has to be explained through science. Loki shows that mythology is still of large influence. In the finale, Loki becomes a deity weaving threads of unrefined time together into Yggdrasil. This resembles the Norns' task in Norse mythology. They are described as three Jotuns responsible for shaping the course of destinies and nourishing the World Tree. In the MCU though, there is now only one Jotun responsible for the flow of time and keeping the tree and it's branches alive: Loki, God of Stories.
In conclusion, more alternate timelines (branches), parallel timelines and dimensions means different rules. Especially if they operate outside of spacetime, like the TVA or the End of Time. Time loops appear to be the norm due to a lack conventional time, yet there is still an irreversible order of events happening. All TVA branches may have spaghettified and thus tied up any loose ends, there might still be a HWR in a branch, as the last one the timeslipping Loki talked to didn't die on-screen. And timeslipping is just another form of timetravel, regardless of Loki going somewhere new or taking his own place.