Since somebody asked me this exact same question in a private message recently, I'll share here what I wrote to them:
1) determine
The verb 'determine' means something close to 'find out for sure'. It's a good verb to use with the idea of an investigation because an investigation is done when people want to find out what happened.
The investigation will determine what really happened.
This is an excellent example to show the meaning/use of 'determine'. The idea is that there are possibilities in mind that must be ruled out. Imagine there's been a a plane crash and an investigation team is called to determine the cause of the plane crash. Before the investigation, nobody knows for sure what really happened. People may have some ideas but they don't know for sure. When you determine something, you kind of close all possibilities except one—the real one. Logically, it's similar to the verb 'conclude'.
In philosophy, determinism is the idea that that there is only one history of the universe and that there are no possible alternate worlds except in your mind. That means that God has 'written' the history of the universe already and everything is happening according to this code—everything is 'determined'. There is only one history, only one set of events, and only one thing that can happen.
Think of an open set of possibilities collapsing into one.
2) identify
If you identify something (verb), you are saying that two or more things are identical (adj.). This is the notion of identity (n.) and the related notion of identification (n.).
The idea of identity is essentially about the sameness of reality. When we look around the world, we look for differences and similarities. Imagine you see a dog outside your house in the morning and then you see another dog a few hours later. How do you know if it's the same dog or a different dog? Both possibilities could be true. Well, you try to identify the dog. You look at the dog and your mind compares what you see with what you've seen before. If the dog has the same size, shape, fur, etc., you believe that it's the same dog that you saw in the morning. You have identified the dog.
Let me put that in a way that a mathematician or a logician would put it: Two things are identical if they share all properties. If you draw two circles, with exactly the same radius, the circles are identical.
Here's another good illustration of the meaning of identify: Imagine a crime has been committed and the police have brought in to the police station a group of men, one of whom committed the crime and the others of whom are totally innocent. The victim of the crime comes into the room to look at the group of men. She is trying to identify the criminal. That means that she is trying to match the mental image, the memory that's in her mind, with one of the real men standing in front of her. This is the notion of identification.
