What kind of cheese is the result of boiling milk with vinegar at home?
The resultant cheese in your first link will be a fresh, soft cheese, nothing like either of the Parmesan or cheddar cheeses mentioned in your second link.  It is also an acid-based cheese, not a made with either rennet or bacterial cultures as are most other cheeses.

Parmesan is a very long aged cheese.

Cheddar is a... well... cheddared cheese (cheddaring is a process which reduces the moisture content of the curds) that is then aged for varying periods of time.

The fresh cheese in your first link will not serve you well in the same roles as either Parmesan or Cheddar.  While I realize these products may not be available easily where you live, they are very distinctive and hard to substitute for with homemade products--they just also not the kind of cheese that is normally made at home.

The home made cheese described is most similar to an unaged feta (although not goat's milk), or a Mexican queso fresco.