When using Express Buy (or 'Buy' for short), users are buying bitcoin directly from Bitaroo. We act as the seller and set the rate, which is why Buy has no buying fees.
When using Trade, users are buying and selling bitcoin from each other. We only provide the platform and facilitate the transactions, which is why there are trading fees on top of the prices you see in the order book.
A good analogy to illustrate the difference between Buy and Trade is buying goods in a convenience shop vs in a supermarket.
Convenience shop (Buy): quicker process (you're in and out very quickly); easier to find what you're after; less products to choose from (making your options easier); higher prices.
Supermarket (Trade): bigger space with plenty of choices and options to choose from; could be overwhelming and complicated if all you want is one item, and you're not sure where it is; lower prices.