Identifiers with this become public properties, whereas those with var become private variables.
Nowadays, const should be used instead of var; if you can’t use const for a specific variable, use let instead.
The access semantics are the same.
When using an identifier with the this keyword, like this.x = 4;, you’re setting a property with the key "x" and the value 4 on the object referenced by this. Since this refers to the instance in the context of a class, such properties become instance members of the class, which means they will be available in each newly created instance of that class. When you use this, it means that your intention is to use it in a class, so you need to instantiate it using the new keyword as shown below.
Example
function Foo() {
  // Variables, scoped to the function. Private access.
  const bar = 'I am bar';
  
  // Properties, set on the instance. Public access
  this.baz = 'I am baz';
  this.secretBar = () => `It’s a secret to everybody: ${bar}.`;
}
const f = new Foo();
console.log(f.bar); // undefined
console.log(f.baz); // "I am baz"
console.log("bar" in f); // false; f does not have the property "bar".
console.log(f.secretBar()); // "It’s a secret to everybody: I am baz.";
  // `secretBar` is in the scope of `Foo`, so it has access to its variables.
 
 
While making a JavaScript class function, I’m using this.
A lot.
But while using that, it’s making me wonder whether it would’ve made a difference to use var instead.
There is a significant difference. You should not create variables with the this keyword that you don’t want to appear in instances of your class, unless otherwise needed.