Which table exactly is the "left" table and "right" table in a JOIN statement (SQL)?

The Left table is the first table in the select. Yes, your two examples are equivalent.

The right table is always the table that you are joining on. So yes, both of your statements are equivalent.

JOIN [Table] ON ...

[Table] is always the right table.

Roughly "left" is the result of everything that appears first in the whole FROM clause when reading from left to right - including the result of other JOINs, sub-queries, VIEWs and STORED PROCEDURES.

Both SQL statements are equivalent because the = operator at the ON part of the JOIN clause is symmetric (if a = b then b = a) so the result is the same no matter the order.

The regular join shows only the lines where the ON clause of the JOIN is true, while the LEFT JOIN shows also the records from "left" if the condition is false (showing NULL for any column from "right" present in the SELECT).

For example:

-- People:           -- Car
id | name            owner_id | model
---+------------     ---------+------------
1  | Paul            1        | Ferrari
2  | Nancy           2        | Porsche
3  | Arthur          NULL     | Lamborghini
4  | Alfred          10       | Maserati

> select people.name, car.model from people join car on car.owner_id=people.id;

name     | model
---------+--------------
Paul     | Ferrari
Nancy    | Porsche
2 record(s) found

> select people.name, car.model from people left join car on 
  car.owner_id=people.id;

name     | model
---------+--------------
Paul     | Ferrari
Nancy    | Porsche
Arthur   | NULL
Alfred   | NULL     
4 record(s) found

> select people.name, car.model from people left join car on 
  people.id = car.owner_id;

name     | model
---------+--------------
Paul     | Ferrari
Nancy    | Porsche
Arthur   | NULL
Alfred   | NULL     
4 record(s) found