Forcible Detainer is that considered a non-payment of rent as well?

A forcible detainer is basically when a lesser period of tenancy has been terminated and they retain possession of the premises after such termination and refuses to vacate after written demand has been made. If that tenant happen to leave behind their belongings the landlord has a duty to provide ordinary care in the protection of such property for a reasonable period then it would be considered abandoned. Note this time frame varies with each State.