ssh 2 different computers behind same router and modem?

You're misunderstanding port forwarding.

You got DOG set correctly... that is External IP-port 22 -> DOG internal IP port 22

For CAT what you want is External IP-port 2222 -> CAT internal IP port 22

You don't want to change any local machine, you just want the router to take requests for 2222 and send them to the correct IP/port combo, which is the internal IP for CAT and its SSH service is running on port 22.

For example this is how I would set it up on my router (your screen will probably look slightly different).

What the above directions say to the router: Take traffic coming from the internet on port 2222 and route it to port 22 of CAT on the local network at local ip address 192.168.1.5.

Another hint: If your router has DHCP turned on, find the DHCP reservations table in your router and add entries to it so that CAT and DOG will always be given the same IP address. DHCP assigns your local IP addresses, and it simply assigns the next available when a device comes online and says "I need an IP". However when you are forwarding ports, you want those local devices to always get the same IP. If they didn't, then one day DOG might have CAT's IP and vice versa. Setting the DHCP reservation would make sure that DOG and CAT always get the same IP.