Zabbix is running on a Master Node and each Client has an Agent. (Yes the master is an external System)
Zabbix can monitor clients active and passive.
Passive means the Master asks the system for data and the system delivers.
This does not always work within special networks where the master can not reach the client.
Then you use active monitoring then the client reports all data in a certain interval to the master.
There can be a master / slave / proxy setup for big scale monitoring solutions. (Google Zabbix HA Cluster Setup for more details)