The zinc cent is as you have stated, with the help of someone starting that damage. Someone dropped or spilled something one the '37, IMHO. Interesting fact; back in the good ole' days, electricians and others that dealt with soldering objects, would clean the head of their soldering irons on old pennies (cents) to remove residue, thus depositing the silver colored solder onto the coin.
Simply put, they are both damaged. The 1937 has something put on it, like solder as mentioned by Mountain Man. The 1984 is showing signs of zinc rot in the 2-3 o’clock position. The missing portion on the left side at 8 o’clock was caused by someone drilling into the coin.
