Technically they both are the same. However, Warehouses are typically meant for storage, where as Distribution Center happens to be much bigger, in the US people call them distribution centers because they do a lot of distribution of products with a lot of high tech equipment with many people executing all kinds of processes, sometimes DCs also provide value added services like Kitting, building Promotional Display Vehicles, Assortments etc.
Also Distribution centers tend to support multiple channels Retail, Ecommerce, Wholesale etc, all these require different Proceses and different systems.
Also DCs tend to be the hubs of Supply Chain, so it is very important the throughput is maintained to its highest and the product moves very fast. The operation is huge with size ranging from 200K SQFT to million plus.
If there are any other specific questions will be happy to answer those.