How does the router know how the client got the address?

Question

Computer networks

1) How does the router know how the client got the address? In the web panel of the router, opposite each client, for example, Manual,DHCP,Static is written. How does he know how each of them got his address because this only happens once when connected to the network?
2) What will happen if you connect 2 hosts to the network and register a different subnet on each of them, for example, from 1-10.10.10.10 to 2-20.20.20.20?

Answer 1

1) The router sees that the client is walking through it with the given address. And about the very issuance of the address, you can just google it . There is no point in rewriting here.
2) At the data link level, they will see each other, of course. But at the network level, they will not be able to interact and will be, as it were, invisible to each other.

Answer 2

1. It all depends on the specific router, but in the general case, you need to remember that DHCP distributes addresses in broadcast packets, just so that everyone knows which address got to whom
2. The question is not correct. It is obvious that there will be two hosts networked with different addresses and subnets. What problem do you want to solve?