The definitions of ALLTM and INF are as follows:
$$\mathrm{ALLTM} = \{ \langle M \rangle \mid \text{ TM $M$ such that $L(M) = \Sigma^*$} \}. $$
$$\mathrm{INF} = \{ \langle M \rangle \mid \text{TM $M$ such that $L(M)$ is infinite} \}. $$
In one of the proofs of undecidability of INF, they reduce $A_{TM}$ to INF as follows:
Given $\langle M,w \rangle$, construct $M'$ : "On input $x$, simulate $M$ on $w$. If $M$ accepts w, then Accept". Clearly, $M$ accepts $w$ when $L(M) = \Sigma^*$. "
Here, the proof for INF proof used the definition of ALLTM to show that the reduction is valid.
Can we use INF and ALLTM interchangeably? If not, what are some crucial differences in these sets?