Yes, they will return the same result. The left join without the where clause would read as show me all the records from the header table and the related items from the details table or null for the details where there are no matches.
Adding a where clause relating the ids effectively transforms the left join to an inner join by eliminating the non-matching rows that would have shown up as having null for the detail part.
In some databases, like MS SQL Server, the left join would show up as an inner join in the query execution plan.
Although you stated that you don't want Venn diagrams I can't help referring you to this question and its answersthis question and its answers even though they are filled with (in my opinion very helpful) Venn diagrams.