Se has to do with living in the moment, being aware of the details of what is happening around you at the current time, paying attention only to the immediate context of the inputs you see rather than looking for any further connections, being physically coordinated, enjoying physical activity, indulging the senses, doing things just because they seem fun, etc.
Si has to do with having present experiences evoke past ones. It automatically compares and contrasts what is currently being experienced with something already inside you, sometimes specific events that bore similarity and sometimes (more often with those with stronger Si) social norms. Those with dominant Si tend to be uncomfortable with how strongly they perceive things to diverge from the norm (how things "break the rules"), whereas those with less mature Si might be more upset when they see strong adherence to a norm that does not make sense. In a tertiary role at least, it leads towards lots of reminiscing and perhaps nostalgia, whereas when stronger it may actively try to return the world to the way it used to be. It has to do with remembering things in great detail, and conducting in depth research so that there is more to recall later. It deals with focusing on the intended goal of a task, rather than looking for other, potentially better, outcomes. Si also seems related to muscle memory, so while it does not have the natural coordination of Si it can train to be better.