Here are some processes that can result in changes of the kind you are asking about.

Movement of rivers. Where they are not channeled and maintained by people, rivers tend to wander. For this reason, many rivers are surrounded by lakes called "oxbow lakes", which lie in old river channels. And sometimes rivers move a lot. For example, left to itself, the bulk of the flow of the Mississippi River would no longer pass through New Orleans, or even through Baton Rouge. Instead, it would be flowing down the Atchafalaya Valley, entering the Gulf of Mexico over 200 km west of the current Mississippi delta.

Expansion of river deltas. Where a river terminates in a lake or ocean, its flow slows greatly, often resulting in silt deposits that slowly build up and become land. The result is that the sites of some major historical coastal cities no longer lie on the coast. This is true, for example, of the site of the ancient city of Ur in Iraq. This site is near the former location of the mouth of the Euphrates River; today it is something like 100 km from the Persian Gulf.

Formation of lakes due to the natural damming of a river by a glacier or a landslide. For example, Earthquake Lake in southwestern Montana was created in 1959 when an earthquake-induced landslide dammed the Madison River.

Formation of lakes due to floods and/or rerouting of rivers. The Salton Sea, a lake in southern California, has formed and disappeared every few centuries due to processes like these.

Changes in vegetation due to climate change. Boundaries between different kinds of vegetation (e.g. forest and grassland) are constantly moving. The most obvious examples of this would be the expansion of deserts in the Middle East and North Africa.

Formation, destruction, and movement of barrier islands by storms. For example, along much of the east coast of the U.S., there are lines of islands a little way offshore. These are essentially piles of ocean-bottom sand created by storms and anchored in place by vegetation. Subsequent storms can greatly alter the shape of these islands and sometimes eliminate them entirely.

Expansion and reshaping of volcanoes due to eruptions. This is the land-based version of your "tiny volcanic islands". Volcanoes mostly grow. Sometimes they blow up. Lava flows can destroy huge swathes of vegetation.

Advance, retreat, and disappearance of glaciers. The terminus of a glacier doesn't sit still. Glaciers shorten and lengthen in response to changing weather and climate. Sometimes a glacier goes away entirely, leaving a valley with a characteristic U-shaped cross section.

As /u/ggchappell notes, the easiest ones involve movement of watercourses, though it's usually only an issue at larger scale than the typical wall map of the world. I make a lot of maps for history books, and that's one of the things I always have to be careful about. I can't make a map of 19th century Oklahoma and Texas showing all the reservoirs constructed since then, or of Chicago showing the North Shore Channel and the Sanitary & Ship Canal. For a map of the Opium Wars or somesuch you'd want to make sure you didn't show the massive modern Macau created by landfill since 1997; historic maps of The Netherlands have to be careful about land reclaimed from the sea. And as you note, any mapmaker showing the Aral Sea or Great Salt Lake must take care not to introduce anachronisms.