I do not claim to be a geologist of any kind of authority on the subject of monoliths and hoodoos. This is my understanding of the difference.

A monolith is a geological feature consisting of a single massive stone or rock, such as some mountains, or a single large piece of rock. 

Erosion usually exposes the geological formations, which are often made of very hard and solid igneous or metamorphic rock. The Tower of Babel is one of the most distinctive sandstone structures in Arches National Park.

An enormous narrow freestanding wall or “fin” of Entrada sandstone, the Tower of Babel is one of the largest monoliths in Arches National Park.

A hoodoo is a tall, thin spire of rock that protrudes from the bottom of an arid drainage basin or badland. Hoodoos typically consist of relatively soft rock topped by harder, less easily eroded stone that protects each column from the elements. They generally form within sedimentary rock and volcanic rock formations.

They are kind of eerie, so they're called "hoodoos" and also have other names, from "fairy chimneys" to "goblins."

Hoodoos or Goblins are one of the most spectacular displays of erosion. They are geological formations, rocks protruding upwards from the bedrock like some mythical beings, conveying the story of hundreds and thousands of years of weather erosion.

Most Hoodoos are made of sandstone, sand-sized particles cemented together by calcite, silica, or iron oxide. They are created by erosion. Rains, running water and strong sand winds slowly chip away the material from the bedrock. As some parts of the sandstone are stronger than others, uneven shapes of remains begin forming. Most of the time Hoodoos have a very hard rock on the top, called the Caprock which protects the softer sandstone layers beneath it from further erosion. That is why Hoodoos usually appear as ‘spikey’, ‘human’ looking formations ranging in size from that of a human to that of a ten story building.

Some of the most spectacular Hoodoos exist in Bryce Canyon National Park in Utah. There, in addition to the erosion modes mentioned above, a process called frost wedging plays a key role in forming Hoodoos.

During the day water from the melted snow seeps into the small cracks in the rocks where it freezes during the night. Water expands as it freezes into ice, it causes cracks to expand even wider. At Bryce Canyon there can be over 200 freeze/thaw cycles each year, which speed up the erosion and formation of Hoodoos. Erosion at the Bryce Canyon proceeds at a rate of 2-4 feet of rock being carried away every 100 years. This means that Hoodoos we see there today will be destroyed in several thousand years by the same process that created them.