Programming

There is no concrete difference between the two options. But in general they will be similar. I think you are talking about these options:

struct Person;
struct Skill;

struct PersonSkills {
    person: PersonId,
    skill: SkillId,
}

vs

struct Person {
    skills: SkillId[],
}

struct Skill;

The main difference that I see is that there is a natural place to put data about this relationship with the "join table".

struct PersonSkills {
    person: PersonId,
    skill: SkillId,
    acquired: Timestamp,
    experience: Duration,
}

You can still do this at in the second one, but you notice that you are basically heading towards an interleaved join table.

struct PersonSkills {
    skill: SkillId,
    acquired: Timestamp,
    experience: Duration,
}

struct Person {
    skills: PersonSkills[],
}

There are other less abstract concerns. Such as performance (are you always loading the list of skills, what if it is long) or correctness (if you delete a Person do you want to delete these relationships, it comes "for free" if they are stored on the Person) But which is better will depend on your use case.