max_connections is a global variable which will retain this value until you change it in
my.ini and restart MySQL service.
Whereas concurrent connections can be measured by
max_used_connections status variable which will vary based number of concurrent connections on your MySQL server.
This value is used to calculate
Highest number of concurrent connections.
i.e. If this value is say 1000 and after sometime if number of concurent connections drops still this status variable will show 1000 until you execute
Flush status query on your server.
To know exactly how many connections are open currently, you should check
Threads_connected status variable.