What is the difference between a equals equals 0 and a equals 0?

One equals is used in an equation which is true, such as 5 + 3 = 8

Equals equals is used in computer programming as a question as to whether 2 things are equal. Like

If x == 4

perform this operation

...

If you are referring to 'C' language programming:

A single equal sign is an assignment, a double equal sign is a comparison.

a = 7; /* An assignment. You are assigning the value of 7 to the variable called 'a' */

if (a == 7) /* A comparison. You are checking if the variable 'a' has the value of 7 */