Most of the time, there seems to be three GENERAL rules:
1.) If you pay for an "off lease" fee with the owner, the owner will usually continue to pay for the care of the horse. i.e, vet, farrier, teeth, worming, etc. So say you pay $200 a month for an off lease...ultimately, the owner would use the money you pay them to upkeep the care of the horse. You just go to the barn and ride.
2.) A FREE off lease means you will not have to pay the owner a monthly fee to ride, but you WILL have to pay for the care and upkeep of the horse. So, teeth, farrier, worming...and if the horse has a bad accident and the vet bill is $3,000? Yikes - it's yours.
3.) No matter what you pay the OWNER of the horse, you will still have to pay to board the horse somewhere. So if it's not a free off farm lease - you'll pay X amount to the owner + a monthly boarding fee to a completely different person. Example: $200 a month to horse owner, plus $800 a month to BARN owner for boarding fee.
Even if the lease price is free - you will still pay board and care. The horse is practically yours, financially. The only difference is the owner can take him or her back any time and you can give him or her back any time things stop working out/you can't afford it.
I considered off property lease to see if it'd help since financially, I can't afford to own my own horse quite yet. Then I realized no matter which way I cut it, I'll be practically paying to own one anyways. Whether or not it's lease fee + board or board + care & upkeep, it's not cheap enough for me! Practically the same thing as owning. You just won't have to worry about selling if you get overwhelmed, and you'll always have someone to turn to if you need help. Either way - still not affordable for me.
If it's in your price range, however, it's a great thing to consider if you want to ease into owning but you're not quite ready to make decisions about care on your own/take on ALL the responsibility. An on farm lease, as you probably know - would be "pay to ride." :)