Love your analogy distinguishing the two.
To also note, Traffic manager is a solution for inter-regional connectivity. Where as the load balancer is specific to one region.
In your example you could just have front end public IP or IP prefix on the LB.
But I understand this is an example to clarify between the two. In real world context your traffic manager would punt traffic between multiple load balancers across Azure or even on-prem regions (banking branches)
Nice article!