Horizontal scaling is distributing the load to multiple physical / virtual machines using a load balancer. Same of distributed systems.
The question is is horizontal scaling same as distributed systems ?
Distributed systems are not horizontal scaling.
The distributed system architecture is about having different components on different machines/places, making them communicate through network. This involves specific design, as you can't completely rely on communication (speed, errors, availability). A main concern also is about distributed transactions.
With horizontal scaling, you have the same component instanciated and executed on different places (but often not far, so they share DB or cache). The component manages the whole transaction, without communicating with the other ones.
A common architecture is to "horizontal scale" the different components of a distributed system, to enhance availability of the overall system ;)