You probably have a secure tenancy if you got your home through the waiting list and have lived there for at least a year. Secure tenants have strong rights.
Flexible tenancies are a new type of tenancy for new council tenants. Your council decides if new tenants receive flexible tenancies
Most councils give new tenants an introductory tenancy for the first year. This is on a trial basis - you can be evicted very easily.
Secure council tenancies can be downgraded to a demoted tenancy in some circumstances. This gives you similar status to an introductory tenant.
Living in temporary housing provided by the council isn’t the same as having a council tenancy. Make sure you know what housing rights you have.