MySQL: No. of Connections
Server Status Variables


  Connections
  
  The number of connection attempts (successful or not) to the MySQL server.


I.e. it is a counter which can increase only. Each attempt to connect to server, both successful and falling, increase it. Each connection, both existing and already broken, is taken into account. So this variable value can be used only for to calculate the average number of connections per some time period.


  Threads_connected
  
  The number of currently open connections.


It is the amount of real external connections in any state. Do not include inner server services connections (sheduler connection, for example).


  Threads_running
  
  The number of threads that are not sleeping.


It is the amount of real connections not in sleeping state, including inner server services connections (sheduler connection, for example).

You can see a correlation between last 2 variables while compare the output of the commands

SHOW GLOBAL STATUS 
    WHERE Variable_name IN ( /* 'Connections', */
                            'Threads_connected',
                            'Threads_running');


and 

SHOW PROCESSLIST;