What is the difference between created and every time edited, created and any time its edited to subsequently meet criteria?

Created:
         
 Evaluate the rule criteria each time a record is created if the rule criteria is met, run the rule, updates to existing records.

Note: With this option, the rule never runs more than once per record.

Created and every time it's edited:
           
Evaluate the rule criteria each time a record is created or updated.If the rule criteria is met run the rule.

With this option, the rule repeatedly runs every time a record is edited as long as the  record meets the rule criteria.

Note: We cannot add time-dependent actions to the rule if you select this option

Created and any time it's edited to subsequently meet criteria:
          
Evaluate the rule criteria each time a record is created, or updated

•  for a new record run the rule if the rule criteria is met.
• for an update record run the rule only if the record is changed form not meeting the rule criteria to meeting the rule criteria.

Note: which this option the rule can run multiple times per record, but it won't run when the record edits are unrelated to the rule criteria.

How to update the filed without relationship?

Trigger is the answer for above question.
By using Trigger we can update the field without relationship.