Based on my reading, a sublet has a beginning and an end (it's a short term rental) executed by the Tenant, with permission from the Landlord. The Landlord cannot withhold such permission arbitrarily. It is an agreement a Tenant enters into when they have to leave for a fixed term, with the intention to return. The new tenant is a "subtenant" under the Lessee. In contrast, an Assignment is a "lease takeover", where the person moving in takes over the rights and responsibilities of the previous Tenant, who abandons his Tenancy. A Landlord may object to or approve the new Tenant - see the form A2 below.
When we first entered into our agreement, we did not have much time to look into the law, and we also had Internet problems. I cared far more about Internet access than I cared for my legal status, but our understanding was that I could either stay for a bit and leave, or pay a bit more and take over the lease, if in my judgement, the conditions were favorable. However, if I will ever be in the same situation again, I'd be looking at the following:
Ontario Tenants Notes on Assignment or Sublet and Offences
CLEO guide
Landlord SelfHelp (PDF)
Sample contracts:
As a Tenant (Lessee), you can use form A2 from LTB (instructions) in an application to either terminate your tenancy if the Landlord does not consent to the sublet or assignment, or to force the "overholding subtenant" to move out if the latter refuses to do so. The Landlord may also use it to terminate a tenancy for reasons of having rejected the application, but they need to have serious reasons.
See also the Sharing Tool and Resources for more help.