estuve means ( i'm been) is the past and takes part of the verb ( estar), it's used for to indicate a place or your mood, or behind a verb, ex ( yo estuve en italia), ( yo estuve mal por ti). Instead (fui) takes part of two verbs ( go) and ( be) that in Spanish is translated such as ( ir ) and ( ser), fui is third person. If you put it in the verb ( ser) means i was, if you put it in ( ir) means, I went.
I hope that my answer was useful for you. A greeting