It seems people get confused, so...
1) - SLIP POTTING is when a tree is in a training pot or in a cheap bonsai pot and is going to be exhibited; a fantastic pot is bought or rented just for the exhibit, with the exact same dimensions as the training pot. Tree changes pot (slips) with no roots being touched.
2 - UP POTTING is going up in size. Peripheral roots are teased, bonsai soil is added to the new bigger pot but the roots are not pruned or cut.
3 - REPOTTING is moving the tree into a training or bonsai pot (in general smaller than the original training pot); roots are exposed, teased, pruned and combed, all or most of the old soil is trashed and new, fast draining bonsai soil is added.
1 is harmless to the tree.
2 when done at the right time is harmless since the stress is minimized.
3 is very stressful to the tree specially if the tree is barerooted. It's done at the window of time appropriate for the species and can easily kill a tree if done wrong.

Slip potting - this would be easy if the tree were growing in real dirt and the roots had grown all the way to the edge of the pot. Then the dirt would all come out in the shape of the pot.

What about more proper bonsai soil, say akadama, lava rock, and pumice? That doesn't cake together and I can't imagine just bringing the whole soil mass. Am I wrong?

Ivan wrote:

I can't imagine just bringing the whole soil mass. Am I wrong?

Established trees ready to being shown usually hold the soil very well.