Washing your body with out intention of Spritual washing which is called Ghusl, does not mean that you will not need Wudhu for Prayers. Wudhu is must before performing Prayers. If you perform obligatory Ghusl like Ghusl of Janabah, then you pray with that Ghusl with out Wudhu. If you perform a recommended Ghusl like Ghusl of Jum'a, then you can pray with it with out a need for Wadhu.
Just shower or washing the body does not mean valid Ghusl.
After you perform Ghusl or Wudhu, your state of purity ( Taharah) continues unless it is broken by wind, urine, stool, sleeping, etc. Any breaking of wind will invalidate the Wudhu and Taharah.