There is a difference. The awbrokermon is the process that must be running that controls all of the broker servers. Within each broker server you may logical brokers which would be controled by the broker server.
On solaris grep for the process awbrokermon first(S45broker60,61,or 65 is the startup script), is it running? If not you will need to start it first. After you start the awbrokermon process, it will normally startup the broker servers unless you have configured it not to. If you startup the awbrokermon process but no broker servers start then check that your awbrokermon config is correct. The config file on Solaris will normally be in the /var/opt/activesw/awbrokermon.cfg or /var/opt/webmethod/awbrokermon.cfg depending on your version. This config file will tell you where all of the broker servers are installed.
If the configs are correct but still no broker servers and the awbrokermon process is running, check for error logs and core files for each broker server.