The government must take immediate action to stop the illegal animal trade by implementing the measures proposed by the UN.
Action implies that the Government should do something about the illegal trade.
Measures are the actual ways in which the government will act to stop the illegal trade.
action = the government will do something to DIRECTLY stop the activity. Send in the police, for example. measure = suggests that government will do something to INDIRECTLY stop the activity. For example, raise the tariff on imports related to the activity.
trade: refers to the actions of everyone in the activity. Hunters, people who transport the hunters, their guides, the wholesalers, retailers, etc. transaction: = singular, such as only 1 buy and sell of an animal.