PHP process manager mode
PHP-FPM, or FastCGI Process Manager for PHP, 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.