Neither one is really correct terminology.
They both mean that you're renting now and (possibly) buying in the future. So, from that standpoint, "lease to own" and "rent to own" can mean the same thing.
The correct terminology is either "lease-option" or "lease-purchase." And there are differences.
A lease-option is a lease accompanied by an option giving the tenant-buyer the right (but not the obligation) to buy. So, at the end of the lease, the tenant-buyer could simply walk away with no further obligation. A lawyer would call this a "unilateral agreement"--it requires an action by one party (requiring the owner to sell) but doesn't require the tenant-buyer to buy.
A lease-purchase is a lease accompanied by a purchase agreement committing both the tenant-buyer and the property owner to conclude the transaction. At the conclusion of the lease, the tenant-buyer would be obligated to buy and the owner would be obligated to sell. A lawyer would call this a "bilateral agreement"--it requires action by both parties--the owner to sell and the tenant-buyer to buy.
Probably a majority of what you see as "rent to own" or "lease to own" are actually lease-options.
"Lease-to-own" and "Rent -to-own" may mean the same thing. Either one can mean a lease-option or lease-purchase.
Lease-option: The seller has to sell but the tenant-buyer doesn't have to buy.
Lease-purchase: The seller has to sell and the tenant-buyer has to buy.
Hope that helps.