What is the difference between investigation and survey ?Feel free to just provide example sentences.

Survey is a particular type of investigation. There is no clear semantic difference between them, rather the difference is in the fields where each term is used.
E.g. the police investigates. Looking into any kind of wrongdoing or a problem to find out who is at fault or to establish a root cause is an investigation.
A survey can be conducted on a group of people to find out some general traits they have (e.g. opinions they hold or anything else that can be used to describe them). Any kind of wide ranging investigation to find out the properties of some group may be described as a survey. It doesn't even need to be about people, you can, for example, survey a bunch of academic literature on a subject in order to make a general overview of what is currently believed about that subject. You can also survey plots of land to determine exact boundaries for the purpose of establishing ownership.