An (entirely fictional and simple) example to illustrate the difference:

SMUGGLING:

Frank lives in Texas in a border town and works for a company driving products between their Mexican and American plants. He becomes friends with a family living just over the border in Mexico. He learns that they are desperate to come to the United States in order to have a better life, but have been unable to acquire the necessary paperwork. Frank offers to help his friends get into the United States by hiding them in his truck on one of his many trips across the border. Once over the border, Frank helps the family get to the home of their cousin, who has been living in the USA for several years now. This is smuggling. Frank helped the family get into the USA and then they were free to establish a new life.

TRAFFICKING:

Now, Frank’s co-worker Fred heard about what Frank had done, and since he had the same job, decided to do the same thing. Fred got to know another family looking to cross into the United States and planned out how he would bring them over in his truck.  However, once Fred got this family across the border he told them that they owed him for helping them since he could get in a lot of trouble for smuggling them over the border. Fred didn’t let the family leave his control. He took whatever documents they had and made them work on his farm to pay him back. They were never able to find out exactly how much they owed him, or the progress they were making in paying him back. This is an example of trafficking.