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No, but eliminating variables is one of several ways to find the value of variables in a system of equations.
Assuming the simplest case of two equations in two variable: solve one of the equations for one of the variables. Substitute the value found for the variable in all places in which the variable appears in the second equation. Solve the resulting equation. This will give you the value of one of the variables. Finally, replace this value in one of the original equations, and solve, to find the other variable.
They are alike because the both have value, they both have variables, and both have numbers. there, happy?
Finding a set of value for the set of variables so that, when these values are substituted for the corresponding variables, all the equations in the system are true statements.
If you replace variables in an expression by numbers (in case there are any variables) and then do the indicated operations, you get a number. That final number is the "value" of the expression.