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What are the subnets, gw address and network masks in bother cases?

The password might be the fact your username is used for the network user name and it has to match exactly.
For RetroNAS for example, I always install Win98 as user "pi" any other name and it never works.
BTW I never see anybody in the network neighbourhood but access direct (i.e. \\retrosmb works as long as I'm user pi and give the correct password). First thing I do is Map a network drive.

Sounds like you are using DHCP to allocate addresses? You must have only one device on your network enabled for DHCP allocation, it sounds like you may have more.

Also, what shows in Network Neighborhood is influenced by which computer is your Master Browser. For example, if your Master Browser is a W2K machine, the Network Neighborhood will be entirely different to if your Master Browser is a Windows 10 machine.

Are you running a simple flat network without vlans, etc.
As Robbert said If the switch is connected to the router, you shouldn't be getting different subnets!
Servers, switches, routers can all have DHCP servers so disable them all except for 1 (keeping it on the router's probably the simplest)
You can type ipconfig /all to find the IP of the DHCP server.

Browsing the network never really worked till Vista. WIn9x and earlier. You can try installing a WINS server (basically a MS cutdown version of DNS) but I wouldn't bother.
Accessing servers by going \\192.168.1.1 (or whatever the IP address) is most reliable way

and as Deano said Win9x doesn't understand NT style domain\username logins. Best to use the same username/password everywhere.
This is because the server will try with the username that's logged into Win9x and if that matches a user on the server it'll work.
but 9x doesn't have the ability to bring up a username/password box to access a share.

PS
You also want all computers on the same workgroup, If the server is a domain controller still make the workgroup the same name as the domain (this helps with the domain\username login format)

I'll describe my setup. I spent a while designing my local network to ensure that everything works and keeps working.

I have about 70 hard drives with IP addresses allocated, since I use a spreadsheet and hard-coded addresses. Note that NAS's and switches also have addresses that need to be unique on your network.

Both NAS's, the switch and the router all come with DHCP servers. I disabled them all except for the router with a range of 2 to 19, for visitors.

For Network Neighborhood, ensure that all machines are in the same workgroup. I use the WORKGROUP workgroup. This is the default for most Microsoft OS's, however some use MSHOME instead. You still need to specify it.

So, to summarise - all machines have the same workgroup. Each machine needs a unique IP address, but the same subnet, and the same gateway address (your router). DHCP should ensure the correct settings. Only one DHCP server allowed.

In your first message you mentioned that depending on where you plug you end up in a different subnet. Could you please provide the specific details of those 2 different subnets ? Is one of them in the 169.254.x.x address space ?