I am building my inventory and I get a grand total of all my cards but then it tells me some of them are distinct? What are distinct cards or what makes a card distinct?

It refers to the total number of different cards in your inventory that does not count multiples.

For example, putting 4 copies of Lightning Bolt in from M10 means you have 1 distinct entry of Lightning bolt. That other number is just the total number of distinct entries.

Thanks a lot! I appreciate the reply!