The difference between Relationship and Related lists on a table.
Is creating relationship between two tables in a dynamic way where the tables are not related by any field. In other words, table don't have any reference field.
To create a relationship navigate to System definition > Relationships
Here specify Query from(From where the data will be fetched) and Applies(which forms the relationship applies to)
For adding further conditions on choosing the table click on 'Advanced' and write the script.
Related List :-
Is creating a relationship between two tables by using reference field.
To create a related list add reference field on the child table that points to the parent table to create a parent child relationship between two tables.
To view the related list configure it on the parent table. Common examples: Change Request field on Change task.
Thus, Related list are created where there are reference fields between two tables while a relationship is between two tables that don't have any reference field.