A fixed term simply means the length of the tenancy is fixed for either 12, 24 or 36 months, with a set start and end date. A periodic tenancy is a rolling tenancy that continues with no end date once a fixed term ends unless another fixed term is agreed.
When renewing your tenancy and your lettings plan, most landlords opt to renew onto another fixed-term contract, for peace of mind and security. Landlords do have the option to go onto a rolling periodic tenancy, but six months' letting plan fees must be paid in advance.