Isn’t SQL A left join B, just A?

No, since it’s a join, it can produce cardinalities greater than 1 for the rows in A. That is, if there are multiple matching rows from B then a row in A will show up multiple times.

Example:

Table A:

id name
-- -------
 1 Alice
 2 Malcolm
 3 Kelly

Table B:

id_a preferred_food
---- --------------
   1 Pizza
   2 Burger
   2 Steak
   2 Menestroni

Then “A left join B” will give you:

id name    id_a preferred_food
-- ------- ---- --------------
 1 Alice      1 Pizza
 2 Malcolm    2 Burger
 2 Malcolm    2 Steak
 2 Malcolm    2 Menestroni
 3 Kelly   null null

In short:

• All rows from A show up in the left join: even 3 Kelly shows up.
• Columns from B will show up with nulls when there are no matching rows in B: row 3 Kelly has null in the last two columns.
• Rows in A may show up multiple times when they have multiple matches in B: row 2 Malcolm shows up three times.