Uh, I think you're drawing a distinction without a difference.
Both the Gospels and Paul say that Jesus showed Himself to His followers after his death and resurrection. In fact, Paul is describing the same resurrection appearances that the Gospel writers would later write down (except, as you point out, in Mark):
(John 21:1-14):Jesus said to them, "Come and eat breakfast." Yet none of the disciples dared ask Him, "Who are You?"; knowing that it was the Lord.
"Jesus then came and took the bread and gave it to them, and likewise the fish.
"This is now the third time Jesus showed Himself to His disciples after He was raised from the dead."""
Paul says in 1 Corinthians 15: "Christ died for our sins in accordance with the scriptures; that he was buried; that he was raised on the third day in accordance with the scriptures; that he appeared to Kephas (Peter), then to the Twelve. After that, he appeared to more than five hundred brothers at once, most of whom are still living, though some have fallen asleep. After that he appeared to James, then to all the apostles."
So Paul - - writing in AD (or CE) 50s - 17 years or so after the resurrection -- is writing about the resurrection appearances that were witnessed by people still alive when Paul was writing. And his accounts square with those that were written down, several decades later, in the Gospels themselves.
Take a closer look at what Paul actually says in 1 Corinthians 15.
Last of all, as to one untimely born, he appeared also to me. (1 Corinthians 15:8)
I don't think you'd argue that Paul's experience on the road to Damascus was anything other than a vision. Yet, writing about it here, Paul uses the same word -- "appeared" -- to describe both his own personal experience and the experiences of Cephas, the twelve, etc. The implication I draw from this is that their experiences were of the same nature as Paul's. Or, at least, Paul thought they were. Paul says nothing here about the apostles touching Jesus, or him eating with them. In fact, later in the same chapter, he emphasizes the spiritual nature of Jesus's resurrection.