- contrabando de animais = smuggling of animals ou animals' smuggling

Smuggling of animals, animal smuggling (not "animals' smuggling)

- Fiscalização de caça ilegal = poach inspection

Maybe "detection of poaching".  Surely there's a better term.

(Note that the verb is "to poach" and the noun is "poaching".) 

- campanhas de conscientização = campaigns of ___?_____  

Maybe "awareness campaigns".  Safety awareness, handicap awareness, etc.

Há alguma diferença entre smuggling and contraband ?

"Smuggling" refers to the act, and "contraband" refers to what has been smuggled or made illegal to possess. 

(The smuggler was found with 20 contraband television sets.)

(The prisoner was found in possession of the following contraband:  $10 in cash, a knife, a box of matches, two syringes, and 10 grams of marijuana.)