SSH Tunnel
SSH tunnel allows you to create the tunnel which is forwarding all connections to the port NNNN of host to the port 22 (SSH) of the remote host.
You can do it with something like Autossh (examples: https://www.everythingcli.org/ssh-tunnelling-for-fun-and-profit-autossh/)
In this case you will find a single port forwarding rule to the host.
Your routing tables will not change and no additional interfaces will be added.
VPN Tunnel
To set up a VPN tunnel, the Layer 3 interface at each end that must have a logical tunnel interface for the firewall to connect to and establish a VPN tunnel. A tunnel interface is a logical (virtual) interface that is used to deliver traffic between two endpoints. What this means is that if you look into your system interfaces using ipconfig(Windows)/ifconfig(Mac, Linux), you would see the a new interface that establishes the connectivity.
In the VPN Tunnel case, the routing tables will have multiple routes for the companies LAN from your default gateway for each of the subnet in the company. There will be routes to your company networks from your default gateway.
You can find the routes setup with the VPN client by running the command netstat -nr
. Run the command with and without VPN connection and you will see the different in routing tables.