Distributed does not mean in-core. Those are two different things.
In-core vs. Out-of-core
In-core means the solver can hold all the data in RAM while it inverts the matrix. Out-of-core means the solver writes a lot of data to storage (HDD or SSD) while it manipulates some of the data in RAM during the solve process, then writes that portion to storage and reads a different block from storage to manipulate in RAM to continue the solve process. This obviously makes the solution take longer since the access time to a block of data in storage is orders of magnitude slower than the access time to a block of data in RAM. That is why it is vital to have as much RAM as the computer (or the budget) can support.
Large models will not solve in-core, so it is vital to have the fastest storage available, which is SSD. If the computer only has HDD storage, installing a SSD is a nice upgrade for large model solving.
ANSYS will always try to run in-core if it estimates there is enough free RAM to do so. A command object can force the solver to run out-of-core if you have some special reason to not let ANSYS use all available RAM, such as when the solution takes tens of hours to run and other tasks need to run on that computer later in the day and you want to reserve some RAM for later use. I have never used that command.
Distributed Memory vs. Shared Memory
Distributed Memory is used when you tick the box Distributed. This setting almost always solves in less time than when you leave the box unticked, which means the solver uses the Shared Memory parallelism. ANSYS Help has an easy to read section explaining these two types of Parallel Processing.
One reason to untick Distributed is to try to get a large model to run in-core after learning that when Distributed was ticked the model ran out-of-core. Large models often solve in less time using the Iterative PCG solver or won't run at all with the Direct Sparse solver. The PCG solver uses less memory to run in Shared Memory than in Distributed Memory so the largest models may require unticking the Distributed box. ANSYS Help has a section explaining how different solvers (Direct vs Iterative) and different memory choices (Distributed vs Shared) affect the amount of memory needed.