Letters are used to represent different things.

You particularly need to understand the difference between an unknown and a variable.

An unknown represents one from a finite set of numbers, each of which satisfies an equation.

\(\displaystyle x^2 - 9 = 0 \implies x = 3 \text { or } x = -\ 3.\)

So cannot be 100 or 19 or anything but one of those two numbers.

A variable stands for any number in a given set, which may be an infinite set, without any further limitation.

\(\displaystyle f(x) = \dfrac{1}{2x + 3}, \text { where } x \in \mathbb R \text { and } x \ne -\ 1.5.\)

We are saying there that the number specified by f(x) cannot be determined until one of the numbers in its domain is specified, any of the numbers in the domain can be specified.

\(\displaystyle a,\ b \in \mathbb R \implies a * b = b * a.\)

We are saying that no matter which two real numbers you specify, the order in which they are multiplied has no effect on the resulting product.

The symbols chosen to represent unknowns and variables are arbitrary. They have no implicit meaning except as defined for a particular purpose.

\(\displaystyle u,\ v \in \mathbb R \implies u * v = v * u\) means exactly the same thing as \(\displaystyle a,\ b \in \mathbb R \implies a * b = b * a.\)

Finally, it was explained to you that x = y is true only under certain conditions. It is not in and of itself a true statement.

\(\displaystyle f(x) = \dfrac{1}{2x + 3} \text { and } f(x) = \dfrac{1}{6y + 3} \implies x = 3y.\)

\(\displaystyle f(x) \equiv \dfrac{1}{2x + 3} \implies f(x) \ne \dfrac{1}{3x + 3}.\)

It has been explained now to you that your questions are better posed in the context of specific texts or specific problems. As it is you jump around from idea to idea and confuse yourself.