The main difference is that a landlord who has let their property under a short assured tenancy has an automatic right to regain possession of it at any time after the fixed term of the tenancy agreement has expired, provided sufficient notice is given to the tenant. Landlords who have let their property using an assured tenancy agreement do not have this right as the tenant has security of tenure.
Landlords who have an assured tenancy agreement must instead wait until particular limited circumstances have occurred giving them grounds to seek a possession order against the tenants (such as the tenants being in rent arrears).
It would be unusual for a landlord to wish to create an assured tenancy rather than a short assured tenancy (although many landlords inadvertently create an assured tenancy by failing to properly follow the rules in relation to the service of the AT5).
If you have any doubts about which type of tenancy you have then you should seek legal advice.