I wanted to know if the mint marks of these two coins are the same because one is just damaged or if they are different? Thank you.
They appear to be small die chips in the mint mark. Two different does used and worn at some point. That would create the different die breaks.
See the link. You may have two different mint mark styles with die chips. 1968 Date Guide - coppercoins.com
According to The Lincoln Cent Resource only one type/style of mintmark was used between 1952 and 1974. https://www.lincolncentresource.com/San_Fransisco_Mintmark_Styles.html
There is more than one die and mint mark used in minted coins. They are the same but they might look slightly different. One might develop a die chip along with other minor issues. Then add in the wear of the die and circulation wear and tear on the coin.
