Isthmus is a narrow strip of land connecting two larger land areas, usually with water on either side. A peninsula is a piece of land that is almost surrounded by water but connected to mainland (via an isthmus). So a peninsula is often defined as land surrounded by water on three sides.
Most commonly, peninsulas are formed via rising water levels due to increased temperatures and typically where the land is at a low elevation. Gradual rise in the water level leads the land to be surrounded by water on three sides, and develop into a peninsula.
The Panama isthmus is a good example of how isthmus is formed. Before this isthmus was formed North America was separated from South America. A series of events like shift in the tectonic plates and volcanic eruption caused the seabed to rise and underwater volcanoes emerged out of the water forming some sort of solid land. These bit and pieces of land were joined together by sediments brought from adjoining land of North and South America. It took millions of years for this Isthmus to come into existence.
Isthmus is derived from ancient Greek word isthmu meaning neck; while peninsula is derived from a Latin word paeninsula, where "paene" means almost and "insula" means island. Therefore, a peninsula, is "almost an island". A peninsula is also called Half-island, a headland (head), cape or island promontory.
The plural of isthmus is isthmuses or isthmi and the plural form of peninsula is peninsulas.
edit Famous Peninsulas and Isthmuses
The Arabian Peninsula is the largest peninsula on earth. It sits on Arabian tectonic plate, which is slowly moving away from Africa towards the Eurasian plate. The continent of Europe is also a peninsula, with the Mediterranean Sea on the South, the Atlantic Ocean on the West, the North Sea and Baltic Sea on the North and Asia to the East.
The Panama Isthmus is the most famous isthmus. Its formation is considered one of the most important geological event to happen on Earth. It had an enormous impact on the climate and environment. It re-routed the currents in both the Atlantic and Pacific Oceans. It directly and indirectly influenced ocean and atmospheric circulation patterns, which regulated patterns of rainfall. It led to migration of livings things from and to North and South America.