Actually the designation "87" was simply the result of a renaming. It happened during one of the times the company was bought and sold. They were and are the same guns, built by the same company, just different owners.
In 1987, production resumed and the designation 37 was changed to 87. Had nothing to do with licensing as the 87's were Ithaca Gun Co guns. You can follow the trail of the serial nbrs here:
http://www.ithacagun.com/pdfs/serialnumbers.pdf
In 1987, serial nbr 870000001 was made. The 87 prefix lasted until 1996 and ended with 870042931.
There is a book written by Walt Snyder about the Ithaca 37's. It is a very worthwhile investment (if you can find one) and a great reference tool.
3 of mine are "87's". I have 1 12ga field gun and 2 Deerslayer 2's that carry the 87 designation. I have Ithacas starting in the late 40's up to right after the switch back to the 37 designation in 1996 and my 87's are as good quality wise as my earlier guns.
The 87's are decent well built guns ! If yours has the red plastic magazine follower, you might want to acquire one of the blued steel ones that are available from IthacaGun or off eBay. I have changed mine over. Occasionally there there have been reports of the plastic followers getting soft from cleaning solvents or just did.
If your gun ever hangs up, or starts dumping shells, it can be simply dirty or the small spring behind the left hand shell stop could be getting weak. All older Ithacas should go through an good cleaning every once in a while.
Here is a link to the field maintenance manual. I would save a copy to your machine and/or print a copy off.
http://stevespages.com/pdf/ithaca_3787.pdf