He’s been here many times(or many a times)? What's the difference? are both correct and interchangeable?

What the other commenters said, but I'd like to add that you can also say 'many's the time'  which sounds a bit old fashioned and implies nostalgia/reminiscing: 'many's the time we had a laugh at the old watering hole' 'many a time' is also a bit nostalgic and old fashioned. 'many times' is casual and informational and likely to be the usage you're looking for in most scenarios 

"many a time" is a much older idiom that means the same thing as "many times". note that time is singular in the expression

either 'many times' for ordinary speech. or if you're being a little bit fancy 'many a time (singular)'. there isn't any 'many a times' in the plural.