Someone will correct me if I get this wrong..
DirtyDan Specifically,
disabling an app
Stops the app from running and prevents it from running again until it's enabled.
cutting network permission
Prevents network connections. I'd always thought that this applies to Java/kotlin code via the applied security policy as that was what I've used myself and understood. I don't know about the use of dynamically loaded libraries, or apps written as web-apps or cross-platform frameworks.
restricting background data under mobile data usage
When the app is in the background, it may still be active and can make network connections, this option restricts those apps using mobile data but doesn't prevent them. Nor does it do anything about connections over WiFi.
turning off background usage under battery usage.
Apps that are "optimized" can/will be stopped when they're not on screen, usually after about a minute in my experience. Apps can request to be excluded and/or the user can toggle the setting such that the app can continue running regardless.