A built-in metric that is provided by a hypervisor or provider (e.g. CPU usage) or a custom metric that the user creates and populates using API calls

An alarm activates when a metric passes a certain threshold.
If you imagine a dashboard for your metrics, alarms are like red lights that light up when conditions change, for example, when there is a problem. 
See Manage cloud alarms and Infrastructure alarms

An alert enables you to configure notifications or actions from alarms.
Alerts are like a worker monitoring a group of alarms; when all the lights for the group are lit up, the alert is activated.
Alerts can trigger action plans.

A sequence of actions to perform on entities on the platform, such as VMs or scaling groups. An action plan is run by a trigger.

A trigger is an alert or a schedule that will run the action plan, for example, during times of increased demand. 

For horizontal autoscaling, create a scaling group for a VM with rules to define how the platform should scale it out.
You can then include scaling operations in an action plan.

Vertical scaling means scaling up, adding more resources to an existing VM, for example, boosting your CPU and or RAM capacity.

Horizontal scaling means scaling out, deploying more VMs when you need more resources.