Hello Alb
Syslog is a standard that is used by many vendors for the purpose of message logging. Events that occur within a system (say a router or a switch) are categorised based on severity level as well as function and are stored in a buffer on the device itself or they are sent to a syslog server. These messages are used to for system management and security auditing as well as for general informational analysis and troubleshooting. Syslog messages are generated by the network devices themselves and are just read by the syslog server.
SNMP is a protocol that is used to collect and organise information about managed IP devices (such as routers and switches) but can also be used for modifying that information to change the device’s behaviour. SNMP differs from Syslog in many ways, but one of the most significant is that SNMP is more active in that an SNMP server can query and even modify specific variables (MIBs) that describe system status and configuration.
Although both are complementary in that they are both used for system monitoring and troubleshooting, their functionalities are quite different.
I hope this was helpful in getting you started off in further researching these useful technologies!
Laz