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That, yes. 99 or 150 years being typical.
Rental = no property rights but usage rights and the rent is all you pay. Comparitavely short term.
Leasehold, for most urban dwellers at least, means you typically pay at a similarly large scale as if getting freehold rights and get significantly better rights with regard to the property than a renter only a) fixed term, b) built-in depreciation because of the fixed term and c) the bastard who owns the freehold has rather poorly regulated rights to stiff you with ground rent, services charges etc.
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As a matter of law, I'm afraid that's all complete cobblers, not least because there is no legal distinction between renting and a lease. They're the same thing. There are short term leases, where there's no premium but a rack rent, and there are long term leases where the lease is granted for a premium and a ground rent is charged. However, they're both leases, they're both tenancies, and the lessee/tenant in both cases is renting the property.
The terms of short term leases and long term leases are often very different. But they're fundamentally the same thing, although admittedly if you have a long lease of more than 21 years you have rights of enfranchisement you wouldn't have with a shorter term lease.
The proposition that 'Rental = no property rights' is simply wrong. If you rent property, you have the right to occupy it in the same way and to the same extent and with the same proprietary rights and interests as someone with a 999 year long lease.
Still not seeing why leasehold systems are, as a matter of principle, 'rotten'. What are you proposing as a (realistic) alternative to leasehold ownership?
I read Bruce’s comment as a fixed period of property rights applying to leasehold whereas freehold is ownership until all propert rights are stripped at the next revolution.