Overall, I seem to have a lot of trouble visualizing what Si looks like. I'm currently on the idea that Si builds a complete image of the situation, while Se focuses on the interactions and only remembers the fragmented images of what it has observed. (of course our minds tend to lie to us a lot and tell us that our fragmented image was complete all along. There's actually a lot of research on how imperfect our memory actually is. Kind of scary when you think about it).
As to what it actually looks like... I can only give examples, mostly of situations where I interact with my ISFJ girlfriend. For example: when we moved in together, both of us had an idea of how we wanted to fill the cabinets.
My idea was to start with some broad categories and put the items in the broad categories, then after putting the obvious things at the correct place, go a level deeper and specify the categories even more. In that way everything was philosofically in the right place.
My girlfriend had a different idea. She sorted things based on how often they were needed and their practical purpose. Then she would put the things that were needed often in an accessible place and the things that were needed less in a harder to reach spot.
In the end we used the best of both worlds, but the most important part is that we had such a different perspective on the whole situation. I was abstract and analytical, while she was pragmatic and practical. It seems to be the recurring theme in all of our interactions (and it's actually a great experience for both of us).
My point is: the difference between Si and Se might be invisible until you start solving actual physical problems. Once you provide a perspective on a concrete example, it can be obvious how much you don't understand each other.
I'm an ISFP so use Se but following from what spaceynyc said about music, I can listen to a song and can remember when I used to listen to it and where I was sat, what I was feeling, what I was looking at etc which is supposedly Si. But in my case I think it's the interaction of Fi with Se. Weirdly, the scenario I thought of when I read the original post was of me sitting in the car listening to Creep by Radiohead. It was weird to see the next post and see someone else had mentioned Radiohead!! But I can remember listening on my silver ipod nano, what was going on in my life at that time, what I really wanted, what we drove past in the car...sometimes I wonder if I am actually an Se user because I think I seem so Si-like at times.
I think Se with dominant Fi can act a lot like Si is described often. The thing is, as an Fi-dominant you're always primarily processing what everything means to you. This means that everything you experience through your Se is seen through this Fi lens.
I actually kind of dislike how Si descriptions focus on "how the experience/memory makes you feel". That's not Si, that is often Si+Fe or Si+Fi.
That said, all descriptions are going to be coloured by the one that wrote it. It's next to impossible for an Se-user to accurately write down the Si thought process. You can theorize about it, but without actually living it, you have no idea what it is acutally like.