the exchange of agreements (contracts)
the completion of that agreement by the seller handing over the title in return for the buyer handing over the money.
Following exchange each side prepares for completion. The seller arranges for existing mortgages to be discharged and execute the transfer. The buyer makes all necessary searches, enquiries about title, pays stamp duty and arranges for any future mortgage. How long each stage takes will depend on the individual circumstances of the property.
Settlement is the same as completion.