Is people smuggling the same as human trafficking?

No, while people smuggling and human trafficking are linked there are fundamental differences between the two. The relevant distinction is that being trafficked is involuntary, whereas people smuggling involves the consent of the individual being smuggled.
 

The United Nations define both in the following terms:

Human trafficking

vs.

People smuggling

"Human trafficking is the acquisition of people by improper means such as force, fraud or deception, with the aim of exploiting them."
 
"Smuggling migrants involves the procurement for financial or other material benefit of illegal entry of a person into a State of which that person is not a national or resident."
 

 

 SmugglingvsTrafficking