In the lecture notes it says:

"An important characteristic of client-server systems is scalability: Horizontal scaling means adding or removing client workstations with only a slight performance impact. Vertical scaling means migrating to a larger and faster server machine, or to multiservers."

This seems to slightly misalign with the conventional definition that I've come across, where horizontal scaling means adding more processors to an architecture (e.g. additional server nodes), and vertical scaling means adding more processing power to existing processors (e.g. chuck more RAM in the server machine).

Pulled from a quick Google search:

"Adding more hardware components to your current server configuration (e.g., adding more RAM or storage to your dedicated server) is known as vertical scaling. Horizontal scaling adds more servers to your hosting configuration to increase its power." (https://www.cloudways.com/blog/horizontal-vs-vertical-scaling/#:~:text=Adding%20more%20hardware%20components%20to,known%20as%20a%20server%20cluster.)

How should we approach this definition for the exam?

vertical scaling = scaling UP, horizontal scaling = scaling OUT. But your thinking is sort of there. Try thinking about it this way:

out = spreading "out" over more machines up = increasing (upping) the compute one a single machine / monolith

I hope this helps :)