How are they similar and how are they different, can both exist, does one have more basis than the other, why are they important?
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> simulation theory
This is a pseudophilosophical idea that we are living in a simulation like our own computer simulations. It’s a fun idea to play with, and is sometimes used in science fiction, e.g. the Matrix films. Some people, especially people in the tech industry, have argued that we should seriously consider that we actually do live in a simulation, but they haven’t really done a great job of explaining what this would mean or why we should believe it to be the case. The biggest problem is that, if we suppose that there is some “real world” that is running our world as a simulation, we really know nothing about what this real world or its methods of simulation are like. People have speculated that we might see things akin to “computer glitches”, but how can we assume that the simulation has the same kinds of glitches as our computers do? After all, if this is all a simulation, then our computers aren’t even real.
> holographic principle
This is something that comes up in certain approaches to quantum gravity. Our current description of gravity (general relativity) does not seem to make sense at very small scales. The other forces (electromagnetism, and the strong and weak nuclear forces) have been described very successfully at small scales using quantum mechanics. So physicists suspect that there must also be a quantum description of gravity that would work at small scales. Gravity is very weak at small scales, so any quantum gravitational effects would only be relevant in some very specific circumstances: in particular, they are expected to play an important role in black holes, the very early universe, and also the overall expansion of the universe. But we only have a limited amount of observational evidence about these things, and it’s not really enough to develop a specific theory and be confident that it’s the correct one. Some theoretical physicists have spent a great deal of time developing plausible candidate theories that would fit what evidence there is. Something that comes up in some of these theories is that the amount of information in, say, a cubic region of the universe is proportional to the area of one of the faces of the cube, rather than the volume of the cube. So you can fully describe the universe in a 2D space, and the other dimension is kind of like a projection. However, there is very little evidence to suggest that this is actually true, and even if it were true, its scientific and philosophical implications are largely unclear. There is absolutely no connection between this idea and “simulation theory”.
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