As you have noticed with vintage radios, there was a separate receiver and a separate transmitter. Part of this was the physical size of the devices. The Heathkit DX-100 was about 100 pounds, and that was just the transmitter!

Most modern radios are transceivers and take care of switching between the 2. Most times without operator intervention.

What if you want to operate a vintage station? How do you connect the 2 to the same antenna?
Great question, and I had to to a ton of research to figure it out. The first thing you need is a dow key relay.

DOW KEY RELAY
What is a Dow Key?
A Dow Key relay is a type of RF coax relay. Dow Key was a brand that specialized in RF equipment. The relays were so popular that everyone called them a dowkey relay. Kind of like Kleenex.

So how does it work?
When you key a transmitter, you want to keep the RF energy from entering your receiver. The transmitter had a built-in relay that sends power to an external plug. This plug is connected to the dow key relay. When the key is powered, it removes the receiver from the antenna and connects the transmitter to the antenna. If you want receiver muting, you should use a dow key with external contacts.

A note on voltage
There were many voltages used for dow keys. Make sure that the one you are using takes the same voltage that is being sent from the transmitter.

Which connector goes to the receiver and which goes to the transmitter?
It is easiest to use a multimeter and check continuity between the top antenna connector and one of the lower connectors.