The trade winds are created by anti-cyclonic systems either side of the ITCZ, meaning a general north-easterly flow from around the coast off the Maghreb countires, turning to an easterly flow around the Azores and a south-easterly flow into the Gulf of Mexico and the Carribean.
They are known as "trade winds" because they were the main facilitator behind the slave trade, taking ships from Europe towards western Africa, where slaves would be bought in exchage for goods, the slaves then sailed to the colonies in the Carribean and around the Gulf, and finally back to Europe laden with colonial products, e.g. sugar.
They do not affect the ITCZ as such. The ascending air in the ITCZ fans out N and S at altitude and creates the high-pressure areas N and S of the ITCZ. It is these high pressure systems that create the trade winds.
Hope this (rather simplified explaination) helps .