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Can you define intelligence?

Yes.

Will artificial intelligence ever become like our intelligence? Yes, and it will have a lot in common with our own intelligence for two reasons: it will be programmed by people who want it to solve problems in much the same way that we solve them (because our ways of doing things are known to work and make a good starting point), and it will have to apply reason in much the same way as we do if it is to be rational, though it should do a much better job than us because it will never become emotionally attached to its beliefs and it will be able to crunch its way through much more information than we can without getting lost in the complexity. In many ways, the difference between our intelligence and artificial intelligence is rather artificial though - we have evolved to become general purpose computers which are Turing complete, so we can go on improving the way we think as we learn better ways of doing things.

Does artificial intelligence think like us? Do we, or other organisms, think like artificial intelligence? Essentially yes. What any intelligent system needs to do, whether it's natural or artificial, is make a mental model of reality (the world around it and the rules by which things interact), and then it has to try to incorporate anything new into that model. If something doesn't fit (resulting in contradictory data), there has to be a fault somewhere in the model which needs fixing. Superior methods of reasoning will lead to more rapid solutions, but even very poor reasoning skills can eventually remove a lot of faults in a faulty model and improve it over time. The mental model of reality includes rules about how to go about doing things, so it can be used to simulate real problems and to solve them in the model before attempting to tackle them in the real world.

How do we differ from artificial intelligence? We're lazy, get bored easily, make mistakes easily, have memory limitations which make it hard for us to handle large amounts of complex information, and we often want to believe things that aren't true. The advantage we have at the moment over artificial intelligence is that artificial intelligence is incomplete, lacking our easy abiltiy to conceptualise things and to relate concepts usefully - this is the sticking point which has held things back for decades.

Can you define intelligence? If I now interpret your first question as a request for a definition, here goes (though I reserve the right to change it if it falls short in any way):-

Intelligence is the ability to conceptualise things and manipulate those ideas in a mental model such that judgements and decisions can be made and tested in the model before the best ones are applied to the external world.

When it comes to judging what's best though, machines will have to take their lead from us. We tend to know what's best for us because it often hurts if we make a mistake. Computers can't be hurt, but they can be programmed to protect us (and other sentient creatures) from harm and to make that the overriding focus of their mission.