zabbix_server.logを見ましたところエラーが出ておりました。

002948:20081215:090528 Starting zabbix_server. ZABBIX 1.1.7.
002948:20081215:090528 Failed to connect to database: Error: Can't connect to local MySQL server through socket '/var/lib/mysql/mysql.sock' (2)

サーバ側の設定内容は以下の通りです。

★----db.inc.phpの抜粋----★

// DATABASE CONFIGURATION

// $DB_TYPE ="ORACLE";
// $DB_TYPE ="POSTGRESQL";
$DB_TYPE ="MYSQL";
$DB_SERVER ="localhost";
$DB_DATABASE ="zabbix";
$DB_USER ="zabbix";
$DB_PASSWORD ="zabbix";

★----zabbix_server.confの設定----★

# This is config file for ZABBIX server process
# To get more information about ZABBIX,
# go http://www.zabbix.com

############ GENERAL PARAMETERS #################

# This defines which server this is.
# Default value 1
# This parameter must be between 1 and 255
Server=1

# Number of pre-forked instances of pollers
# Default value is 6
# This parameter must be between 6 and 255
StartPollers=6

# Number of pre-forked instances of trappers
# Default value is 5
# This parameter must be between 2 and 255
StartTrappers=5

# Listen interface for trapper. Trapper will listen all network interfaces
# if this parameter is missing.

#ListenIP=127.0.0.1

# Listen port for trapping. Default port number is 10051. This parameter
# must be between 1024 and 32767

ListenPort=10051

# How often ZABBIX will perform housekeeping procedure
# (in hours)
# Default value is 1 hour
# Housekeeping is removing unnecessary information from
# tables history, alert, and alarms
# This parameter must be between 1 and 24

HousekeepingFrequency=1

# How often ZABBIX will try to send unsent alerts
# (in seconds)
# Default value is 30 seconds
SenderFrequency=30

# Uncomment this line to disable housekeeping procedure

#DisableHousekeeping=1

# Specifies debug level
# 0 - debug is not created
# 1 - critical information
# 2 - error information
# 3 - warnings (default)
# 4 - for debugging (produces lots of information)

DebugLevel=3

# Specifies how long we wait for agent (in sec)
# Must be between 1 and 30
Timeout=5

# After how many seconds of unreachability treat a host as unavailable
#UnreachablePeriod=45

# How ofter check host for availability during the unreachability period
#UnavailableDelay=15

# How ofter check host for availability during the unavailability period
#UnavailableDelay=60

# Name of PID file

PidFile=/var/run/zabbix/zabbix.pid

# Name of log file
# If not set, syslog is used

LogFile=/var/log/zabbix/zabbix_server.log

#Location for custom alert scripts
AlertScriptsPath=/var/lib/zabbix/

#Location of 'fping. Default is /usr/sbin/fping
#FpingLocation=/usr/sbin/fping

# Frequency of ICMP pings. Defauls is 30 second.
#PingerFrequency=30

# Database host name
# Default is localhost

#DBHost=localhost

# Database name

DBName=zabbix

# Database user

DBUser=zabbix

# Database password
# Comment this line if no password used

DBPassword=zabbix

# Connect to MySQL using Unix socket?

#DBSocket=/var/lib/mysql/mysql.sock

監視Type：「ZABBIX AGENT」か「ZABBIX AGENT(active)」ですが
インストールするモジュールが違うのですか？
それとも、AGENTかサーバの設定によって違いがでるのでしょうか？

クライアント側の設定は以下の通りです。

★----AGENTの設定----★

# This is config file for zabbix_agentd
# To get more information about ZABBIX, go http://www.zabbix.com

############ GENERAL PARAMETERS #################

# List of comma delimited IP addresses (or hostnames) of ZABBIX servers.
# No spaces allowed. First entry is used for sending active checks.
# Note that hostnames must resolve hostname->IP address and
# IP address->hostname.

Server=192.168.52.75

# Server port for sending active checks

ServerPort=10051

# Unique hostname. Required for active checks.

Hostname=pct052212.hon005.local

# Listen port. Default is 10050

ListenPort=10050

# IP address to bind agent
# If missing, bind to all available IPs

ListenIP=192.168.52.212

# Number of pre-forked instances of zabbix_agentd.
# Default value is 5
# This parameter must be between 1 and 16

StartAgents=5

# How often refresh list of active checks. 2 minutes by default.

#RefreshActiveChecks=120

# Disable active checks. The agent will work in passive mode listening server.

#DisableActive=1

# Enable remote commands for ZABBIX agent. By default remote commands disabled.

#EnableRemoteCommands=1

# Specifies debug level
# 0 - debug is not created
# 1 - critical information
# 2 - error information
# 3 - warnings (default)
# 4 - for debugging (produces lots of information)

DebugLevel=3

# Name of PID file

PidFile=/var/tmp/zabbix_agentd.pid

# Name of log file.
# If not set, syslog will be used

LogFile=C:\zabbix\zabbix_agentd.log

# Spend no more than Timeout seconds on processing
# Must be between 1 and 30

Timeout=3

####### USER-DEFINED MONITORED PARAMETERS #######
# Format: UserParameter=<key>,<shell command>
# Note that shell command must not return empty string or EOL only
#UserParameter=system.test,who|wc -l
### Set of parameter for monitoring MySQL server (v3.23.42 and later)
### Change -u<username> and add -p<password> if required
#UserParameter=mysql.ping,mysqladmin -uroot ping|grep alive|wc -l
#UserParameter=mysql.uptime,mysqladmin -uroot status|cut -f2 -d":"|cut -f1 -d"T"
#UserParameter=mysql.threads,mysqladmin -uroot status|cut -f3 -d":"|cut -f1 -d"Q"
#UserParameter=mysql.questions,mysqladmin -uroot status|cut -f4 -d":"|cut -f1 -d"S"
#UserParameter=mysql.slowqueries,mysqladmin -uroot status|cut -f5 -d":"|cut -f1 -d"O"
#UserParameter=mysql.qps,mysqladmin -uroot status|cut -f9 -d":"
#UserParameter=mysql.version,mysql -V