I've looked at a few videos about installing a new toilet and I've seen this types of connections:
Toilet either inserts and bolts to a base like this:
Or the S pan is inserted into another tube like this:
My own toilet however looks like this:
I have a hard time matching what I see with my own toilet with what I see online. I suppose at different times there were different methods. Does anyone know what am I dealing with in my case? I suspect that these days the seal is made of rubber and in the past they used something like silicon, which turned black over time. Thus the difference between 2nd picture and 3rd.
I have tried calling a few plumbers, but they seem to have plenty of work and are in no rush to assist me, so I'm thinking of connecting a new toilet myself if I can figure out the connection between the S pan and waste pipe.