is that torus is a topological space which is a product of two circles while Torah is a specially written scroll containing the five books of Moses, such as those used in religious services.

As a proper noun Torah is

the first five books of the Hebrew Scriptures, attributed to Moses and therefore also known as the Five Books of Moses.

is that torus is torus (shape) while monkey is any member of the clade simiiformes not also of the clade hominoidea containing humans and apes, from which they are usually, but not universally, distinguished by smaller size, a tail, and cheek pouches.

As a verb monkey is

(label) to meddle; to mess with; to interfere; to fiddle.

As nouns the difference between hyperboloid and torus

is that hyperboloid is a particular surface in three-dimensional euclidean space, the graph of a quadratic with all three variables squared and their coefficients not all of the same sign while torus is torus (shape).