Injective or one-to-one? What is the difference? What is the difference between the terms 'injective' and 'one-to-one', 'surjective' and 'onto', and 'bijective' and 'isomorphic'?
Let $f:A\to B$

Injective/one-to-one: $f(x)=f(y)\implies x=y$

Surjective/onto: for all $b\in B$, there is an $x\in A$ with $f(x)=b$ (basically, all elements of the codomain are represented by $f$)

Bijective: $f$ is both injective and surjective

Isomorphism: a bijective map between two algebraic structures
Injective and Surjective has been given already, the differens between isomorphism and bijection is that for a bijection $f$ versus an isomorphism $\phi$
we have that $\phi(a\cdot b)=\phi(a)\cdot\phi(b)$ while for for $f$ do we not have it, for a bijection we can have $f(a\cdot b)\neq f(a)\cdot f(b)$

Examples of them are $f:R_+\to R_+$ where $f(x)=x^2$, this is a bijection but
$$f(a+b)=(a+b)^2 =a^2+2ab+b^2 \neq a^2+b^2 = f(a) + f(b)$$

Let $\phi:Z\to 2Z$ be an isomorphism with $\phi(a)=2a$ then
$$\phi(a+b)=2(a+b)=2a+2b=\phi(a)+\phi(b)$$