How many terms are in the polynomial abcd+e-h^2?

Short answer 3.

Terms are defined very informally as letters and numbers or a combination of both which are added and subtracted from each other. Terms can be like or unlike. Like terms can be combined to reduce the number of terms.

Discussion and Examples
The variables must have the same variables and powers on those variables to be called like terms.

Example One: 5x^2 + 4x^2 are two like terms. They can be reduced to 1 term
9x^2

Example Two: 5x^2 - 4x^2 are two like terms. They can be reduced to 1 term x^2

Example Three: 5x^2 + 4x are unlike terms. The powers are not the same. Nothing can be done. The question is the answer. There are 2 terms.

Example Four: Your example abcd + e - h^2 There are no variables in common. Nothing can be done. The question is the answer. There are 3 terms.

3 terms <<<< answer.

The last table represents a linear function.