Is equality of two fractions ( like $2/10$ and $1/5$) really equality or equivalence?

Whether $2/10$ and $1/5$ are equivalent or equal depends on how you define the meaning of the formal expression "$a/b$".

If $a/b$ is just a convenient way to write the ordered pair $(a,b)$ of integers when you are discussing the rational numbers, then those two fractions are equivalent - they define the same rational number.

If $a/b$ is just a way to write the rational number that solves the equation $bx=a$ then those two fractions are equal.

In an application they may not even be equivalent. Kids are taugh to model "$1/5$" as "cut a pie in $5$ parts and take $1$ of them". That is not the same physical operation as "cut a pie in $10$ parts and take $2$". That lack of equivalence is even clearer for the commutativity of multiplication: two kids with three cookies each is not the same as three kids with two cookies each even though the number of cookies is the same.

Construction of the field of rational numbers $\mathbb{Q}$, from the integers $\mathbb{Z}$, may help. In this construction, we deal with equivalent classes $[(a,b)]$ for $b\ne 0$, defined by $$[(a,b)]=\{(x,y)\in\mathbb{Z}\times(\mathbb{Z}-\{0\}): ay=bx\}. $$

Therefore, for example, the fraction $\frac{1}{5}$, is equal to the class $[(1,5)]$ which also contains infinitely many elements like $(2,10),(3,15),\ldots$ and all of this elements are a representation of the same class, namely $\frac{1}{5}$.

$\dfrac2{10}$ and $\dfrac15$ denote the same rational number. As rationals, they are equal. As fractions, up to your taste.