A syslog entry is generated by the device as a notification of something happening on the system. An example is that a NAT translation was created.

An SNMP trap is a log entry that is generated by the system that maps from a MIB. An example is a BGP session went down (which may or may not also be a syslog entry). Typically you use traps if you need something specific to be logged.

The logging host can used for both.

Hope that helps.