The difference between Absolute value and Modulus
When used as nouns, absolute value means for a complex number a+bi, the principal square root of the sum of the squares of its real and imaginary parts, \sqrt{a^2+b^2}. denoted by  , whereas modulus means the base with respect to which a congruence is computed.
check bellow for the other definitions of Absolute value and Modulus

Absolute value as a noun (mathematics):
For a complex number a+bi, the principal square root of the sum of the squares of its real and imaginary parts, \sqrt{a^2+b^2}. Denoted by  .
Examples:
"The absolute value x of a real number x is <math>\sqrt{x^2}</math>, which is equal to x if x is nonnegative, and −x if x is negative."

Modulus as a noun (mathematics):
The base with respect to which a congruence is computed.

Modulus as a noun (mathematics):
The absolute value of a complex number.

Modulus as a noun (physics):
A coefficient that expresses how much of a certain property is possessed by a certain substance.

Modulus as a noun (computing, programming):
An operator placed between two numbers, to get the remainder of the division of those numbers.