Lots of vague terminology used here.
To be precises, the IP addresses you will see are the IP addresses of the incoming interface of the router at each hop along the path towards your destination. Incoming interface meaning: the interface on which a router receives your traceroute-packet.
Small fact. TCP/IP is a little weird in addressing. Not every device has an IP address. No, every interface on every device has its own IP address. Therefor some devices can have multiple IP addresses. In general routers have multiple IP addresses, while end-systems (PCs, mobile devices, servers, etc) have only one IP address.
To make matters more complex, you can even create "imaginary" interfaces to add more IP addresses to a device (aka loopback interfaces). Or you can assign multiple addresses to an interface (aka secondary addresses). Or you can use less IP addresses (borrowing the IP address of another interface, aka "unnumbered").
This last paragraph was just added to confuse you.