In real life, Shovels are used for digging, lifting, and moving materials such as coal, sand, snow.
Entrenching Tools (known as the Military Shovel in-game) are collapsible shovels used by militia forces for a variety of military purposes.
Spades (known as the Shovel in-game) are shovels used for digging/removing earth and fixing soil.
Despite their names, the Shovel and Undertaker Shovels models are actually supposed to be vice-versa. The Shovel in-game, as mentioned earlier, is a Spade, while the Undertaker Shovel is a normal shovel.