"The porter comes out of that hotel in which foreign tourists sleep."
Translation:A portás abból a szállodából jön ki, amelyikben külföldi turisták alszanak.
There's no difference in meaning. "Alszanak" is the preferred form in standard Hungarian, but I don't think "aludnak" is considered incorrect.
It is an interesting verb indeed. I am guessing, there are remnants of some ancient conjugation or something still visible in there.
The infinitive is definitely "aludni". But there are 2-3 forms of the conjugation and sometimes several or all of them can be valid in a situation.
"Alusznak", "aludnak", "alszanak". - all the same.
The "alud..." form is used in the past tense. In fact, probably in all situations that are not the simple present indicative. That is, in conditional ("aludnék"), imperative ("aludj"), and all combinations thereof ("aludhattam volna").
So, if I am correct, that leaves us the simple present indicative where there can be confusion, in some of the persons.
More irregularity comes in when we create other words from "aludni". A "v" sound may pop in:
"alvás" - sleeping (a noun, or gerund)
"alvó" - sleeping (present participle)
This is similar to how "enni" and "inni" behave in the same situation. Basic functions of life, obviously.