How to properly define data models in TypeScript?

Question

I am teaching a class on TypeScript basics and I realized something that is really confusing to students and also to me. If I define my TypeScript data model like this

interface Person {
  name: string;
  age: number;
}

interface Teacher extends Person {
  subject: string;
}

interface Student extends Person {
  grade: number;
}

I cannot actually do the following which my students expect to by possible from experience with other languages such as Java, C# etc.

const people: Person[] = [
  { name: "Alice", age: 30, grade: 100 },
  { name: "Bob", age: 25, subject: "Math"},
];

I would argue, ther extends does not create a proper subtype/supertype relationship. It only copies properties from one type to onether. To make this work you need to do this:

interface BasePerson {
  name: string;
  age: number;
}

interface Teacher extends Person {
  subject: string;
}

interface Student extends Person {
  grade: number;
}

type Person = Teacher | Student;

But I am unable to explain to my students why extends works this way. And also, I am not even sure that my solution is the prefered one. Am I getting it completely wrong and there is a better way to structure data models?