Yes, they are different. For example, language seems to be quite lateralised. So in most people language processing mostly occurs on the left-hand side of the brain. So, yes, they are different, but, again, beyond very simple single things like language processing they do not seem to be consistent simple describable differences between the left and right sides of the brain.
"Both sides of the brain are implicated in almost every thing that we do"
Things like the left side does all the consistent thinking and the right side does all the emotional thinking is certainly wrong. There is no evidence to support any of those assertions. Both sides of the brain are implicated in almost every thing that we do. Language is somewhat exceptional, but there are language responses in the right hemisphere. So, are they identical? No. Is there an overarching simple account of how they’re different? No.
The fact that language is lateralised leads people to generalise from that to a whole bunch of other kind of ways of thinking. For example what would it be like to think without language and then generalise from that. But most of these things are wild generalisations and speculations, which go well beyond any evidence that we have.
"There are a huge amount of inter-connections between the left and right hemispheres, through a thing called the corpus callosum"
The brain works in totality. There are a huge amount of inter-connections between the left and right hemispheres, through a thing called the corpus callosum, which is like this thick ribbon cable.
Even when you’re speaking you’re using both left and right hemispheres. You’re processing multiple aspects. It just seems that the actual words seem to be less lateralised for most people. But there is a lot more to speaking than just words. Even speaking is a bi-lateral activity.
There is some evidence that some sorts of emotional processing occurs more on the right, but what seems to happen is that people, quite naturally, extrapolate beyond the data to arrive at a wide range of generalisations about men and women, about black people, about left and right… It’s a human tendency to notice a small difference and then line up a comprehensive account of global differences from those small observations.
As neuroscientists we have to point out when these extrapolations and generalisations go beyond the evidence that is available.