The difference between entrapment and investigation is that investigation is the process of gathering needed information to uncover any criminal activity or crime.
Entrapment is when a person is induced by law enforcement to commit a crime that the person otherwise wouldn't have committed.
The legal defense of entrapment is when a defendant argues that they were induced by a government agent such as a police officer to commit a crime which they wouldn't have otherwise have committed.
Investigation is the gathering of any evidence and information about a crime or potential crime.
The methods of gathering evidence or information for investigations can include interviewing of witnesses, surveillance, analyzing any evidence and using undercover operations.
legitimate investigations, even if they happen to involve any undercover work, are considered lawful in most cases as long as law enforcement does not induce a person to commit a crime they wouldn't have otherwise committed.
An example of entrapment would be that an officer going undercover and repeatedly pressures a person to buy drugs from them, even though the person had no prior interest in drugs.
Or a police officer threatens someone with arrest unless they agree to commit a crime.
If a court happens to find that the entrapment occurred then charges against the defendant who was entrapped may be dismissed.