Depending on the examples in question, there's going to be a few different options, I'll discuss two common/possible ones here.

(1) For balanced rocks, or as their often referred to in a paleoseismic context precariously balanced rocks or just PBRs, these often form in-situ. As described in a variety of publications (e.g., Bell et al., 1998, Balco et al., 2011 with most referencing the Twidale, 1982 book - Granite Landforms with respect to formation mechanisms for PBRs), one common way they can form is basically having a series of vaguely spheroidal shaped boulders in the subsurface defined by sets of intersecting fractures (which form via exhumation jointing, spherodial weathering, etc) surrounded by looser regolith (i.e., much more broken up rocks). As weathering and erosion continues, the looser bits get eroded away, but the boulders (i.e., the corestones) get left behind, and if they're stable, they'll end up staying in their stacked position as the surrounding regolith is evacuated. The Balco et al PDF has a schematic diagram to help visualize this process in their figure 2.

(2) Another possible option are glacial erratics. These are large rocks that are dropped by large ice sheets and glaciers. These were rocks that were picked up (or fell into) a large ice sheet/glacier and transported, usually significant distances, until they were dropped by the ice sheet/glacier, usually as a result of melting. Most erratics don't appear as balanced rocks (more just kind of large, random boulders, often in areas that otherwise do not have many exposed rocks), but theoretically it's possible for a glacial erratic to end up as a balanced rock.

In terms of distinguishing between the two, classic PBRs usually will all be the same rock, i.e., the individual boulders balanced on each other will be largely derived from the same original bedrock and have the same composition, etc. Also, in a given area, there will probably be several PBRs as their formation reflect the right sets of conditions and processes that allow for their formation (and thus you would likely expect it to have happened in more than one spot in that area, though not always). In contrast glacial erratics, by definition, are very different rock than the surrounding bedrock. Similarly, a stacked erratic is probably going to be just one rock high, i.e., a single glacial erratic sitting on top of the local bedrock, as the ability to form actual columns of corestones (like with in-situ formed PBRs) is not really present. Also, while you might expect to see groups of erratics in a particular area, you wouldn't necessarily expect groups of balanced erratics as an erratic ending up as a balanced rock is going to be a bit more "by chance" as opposed to by process like with traditional PBRs.