From pictures I’ve seen before, they tend to be near other, bigger land masses (like near a beach) or clusters of islands where the sea is shallow. The most definitive characteristic is the rocky protrusions that seem to spring from the water suddenly, straight up like a muffin top capped with trees; the sides are sheer rock and does not taper gradually down to sea level. Often, like in the picture, this is near some very low lying sandy beaches. You can also see how the sea has weathered the sea-level part of the rock inward a little bit.
Is there a name for this specific type of rock formation, or the cluster (including beaches and rocks and lagoons) in which it is sometimes found with?
Hard to tell given the angle, but the size and low altitude of the individual islands and their apparent coral base looks like you might be looking at an atoll: Atoll - Wikipedia.
Atolls are usually circular around a lagoon. Some are all that’s left of an eroded or sunken volcanic cinder cone. There often is very little in the way of structure or topography.
The picture in the OP sure looks like the region around Palau. Its islands are coralline reef structures, often karstic with precipitous ridges and poor soils. They typically have that distinctive mushroom shape, the result of the limestone being undercut at sea level to form an overhang.
Sorry, I don’t know of a formal term beyond mushroom-shaped. They are curious and quite beautiful.
As far as I can tell there is no specific name for those “types” of islands beyond “Emergent Coastline”. Emergent coastlines are characterized by sea cliffs (as seen in the photos), and paucity of beaches (as barely seen in the photos).
An “emergent coastline” simply means that the sea level is decreasing relative to land (in this case, the islands). In the case of Palau, the islands are emerging because they are located along an active tectonic margin–in this case, the Palau Trench, where the Pacific and Philippine plates meet.
Well, strictly speaking they aren’t “stacks” unless you can demonstrate a karstic origin. This isn’t unlikely, since limestone and water are a great recipe for karst, but nothing from that photo suggests that they are karstic. These islands look like the result of tectonic (uplift) rather than groundwater processes.
