I've always found sliding in pizza occurs when the moisture in the layers is too different. The cheese is too dry and so it sticks together, the sauce is too wet and so it slides (the toppings can be either). If everything is a bit drier, it sticks together well and can be bitten apart. If everything is a bit moister, it tends to slide apart more easily and won't tug on the rest of the slice that much.
As for why the same ingredients or same brands can sometimes stick, and sometimes not - moisture isn't as tightly controlled as some of the other variables. Cheese in particular can have different levels of moisture from variables in how it was stored - the ice crystals driven off of (or scraped back onto) frozen pizza, or whether a bag of shredded mozzarella breaks into fluffy dry strands or packs into moist clumps in the bag... or tries to melt back into a solid block. Or the settling of sauce, if the denser clumps sink and the thinner liquids end up closer to the top, the first pizza and the last might have subtly different amounts of liquid to deal with.
The level of moisture might also be related to other variables being not so tightly controlled - a little bit more or less sauce or cheese (like, teaspoon-ish) might not be noticed in even professional contexts, or something like the proportion of longer strands to little crumbs of cheese in even the same amount might affect how they interact with each other on a pizza.
the simplest way to fix it is mechanically - mixing part of the cheese into the sauce. This helps add moisture to the cheese, since it is coated in the sauce, and helps dry the sauce (less cheese on top means the sauce is more exposed). The cheese and sauce stick better to each other for being slightly intermixed, and stick better to the crust for being a bit more homogeneous. This has the benefit of not needing to change proportions, if you like a certain ratio.
Toppings, I have always found, are better being partly submerged under the cheese and through the sauce, since they have access to both the oven's heat for browning, and the moisture from the sauce so they don't dry out. It also helps mechanically prevent sliding, interrupting the layers and providing gaps and anchors (depending on topping and relative moisture).
If dealing with a frozen pizza, particularly one I'm adding toppings to, I would sprinkle drops of water on top to make sure the whole thing is moist. If the cheese dries out, it also prevents moisture from leaving the sauce... so more likely leading to slipping. If it stays moist, the problem is much less and it mixes with the sauce better on its own - and its easier to add moisture than remove it.
As for delivery pizza, there's no fix I know of, since it's already made and ready. Ah, well, it tastes good anyway, and it's convenient enough to put up with occasional mishaps.