Was the election of 1948 primary system or caucus system or both?

Neither.

Both primaries and caucuses existed back then, but far fewer of them, and they held almost no sway in who got elected.

A politician might enter a few primaries (and occasionally a caucus, perhaps) just to show he was a serious candidate and that he had voters willing to vote for him. But the primaries did not have a lot to do with how delegates were assigned. The party bosses in different states picked the delegates, for the most part, or were delegates themselves.

Then the delegates would nominate potential candidates from the floor of the convention, and in back rooms party bosses would decide who to back and get the delegates they controlled to go along with whoever they chose.

Neither as they have become used today. Candidates declared, campaigned and went to the convention where a candidate was chosen by many ballots at times. Was far more interesting through the 1960s and it was not as tiring.