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Formulas recognize information mainly from the User Interface (or UI) which deals with the 15 digit ID format.
When there is an ID with 18 Digits, that ID is usually from an export or another program that uses API integrations to send and receive the information.
With Formulas, the 18 Digit IDs are not recognized in the system because they are not in the UI.
An example of an 18 Digit ID formula that would not populate the information correctly would be:
IF(CreatedById = "00Xx0000000XxXxAAW" , "This will work" , "This will fail")
This formula field would always display "This will fail" because the formula is looking for an ID in the system that it would never find.
However, using the 15 Digit ID if the formula read as follows:
IF(CreatedById = "00Xx0000000XxXx" , "This will work" , "This will fail")
Then the fields would display "This will work" when the record was created by the user whose ID matches that ID because the system would be able to find it.
See Also:
Tips for Building Formulas
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