PHP-FPM provides several management modes for its worker processes. These modes determine how PHP-FPM will create, maintain, and recycle the child processes that handle PHP requests. The mode is set using the `pm` configuration directive.
`dynamic` (default)
In the `dynamic` mode, PHP-FPM dynamically adjusts the number of spawned child processes based on the demand, and controlled by the following directives:

`pm.max_children` | the maximum number of children that can be alive at the same time
`pm.start_servers` | the number of children created on startup
`pm.min_spare_servers` | the minimum number of children in 'idle' state (waiting to process). If the number of 'idle' processes is less than this number then some children will be created
`pm.max_spare_servers` | the maximum number of children in 'idle' state (waiting to process). If the number of 'idle' processes is greater than this number then some children will be killed
`pm.max_spawn_rate` | the maximum number of rate to spawn child processes at once

Benefits include automatic adjustment of the number of child processes based on demand, ensuring optimal resource utilization. This is especially useful for servers with fluctuating loads.
`static`
In the `static` mode, PHP-FPM maintains a fixed number of child processes. This number is specified by the `pm.max_children` directive. Benefits include consistent memory usage due to a constant number of child processes. This is ideal for servers with stable loads.
`ondemand`
In the `ondemand` mode, no children are created at startup. Instead PHP-FPM will spawn child processes only when needed, i.e., when there's an incoming request that needs processing. The maximum number of children that can be alive at the same time is controlled by `pm.max_children` directive. Processes are then terminated after being idle for a specified amount of time by the `pm.process_idle_timeout` directive. Benefits include reduced memory usage during periods of low or no traffic. Ideal for servers with intermittent loads or applications with unpredictable traffic patterns.
The best mode for your application may vary based on the server's available resources, traffic patterns, and specific application characteristics. It's essential to monitor and fine-tune the settings to achieve optimal performance.