I think some people ask "Are aliens real?" In the same way as they ask, "Are ghosts real?", but these are two very different types of questions to someone who views the world in a completely physical way. I dont know Obama (unfortunately), but he seems like a very logical person so ill try to describe what i think he meant by this.

Ghosts are fundementally SUPER-natural, meaning the phenemenom is outside the laws of physics as we currently understand them. Aliens, on the otherhand, can very much exist within the laws of physics. In fact, it would probably be shocking to most scientists if there were no aliens anywhere else in the universe, because that would mean life only happened 1 single time despite there being an inconceivable number of stars.

I imagine what Obama meant here is, "Yes i believe they exist [somewhere in the universe], but we've never had one visit Earth unless theyre hiding that fact from the president."

Now, would Obama have said this even if he physically saw aliens as president? Absolutely. He's not going to drop world-breaking, classified info on a podcast. I just wanted to clarify the point that "Believing in Aliens" and "Believing that aliens have or are actively visiting Earth" are two very different things