For a retailer such as Amazon or Wal-Mart:
Sell-in: how many units of a product is a manufacturer selling into the retailer
Sell-out: how many units of a product is selling out to the customer (from the retailer)
Sell-through is the same as sell out. They just invented it to confuse you.
For a manufacturer:
Sell-in refers to sales from manufacturers to distributors. In this case, a global manufacturer may have one or two national distributors, especially with marketing subsidiaries.
Sell-through is sales from these Distributors to Retailers. There may be as many as 1000 retailers from micro Mum n Pop shop type retailers to large chain e.g Best Buy type retailers with several outlets. There will be every retailer type in between as well. Usually, distributors will only sell to Retailers buying in bulk at a decent price. These retailers may also not be able to buy directly from Manufactures and will have to go through Distributors because of MOQs and other requirements imposed by manufacturers.
Sell-out is sales from these Retailers to end consumers. e.g someone walks into a Bestbuy to purchase a product.