Definition
A managed debugger such as the one in Visual Studio or Rider attaches to a Mono player, breaks at a line of C#, and shows every variable. A native debugger such as x64dbg or the one in IDA attaches to any process and works on machine code. Both can set breakpoints, change values, and skip over instructions while the game waits.
Relevance
A debugger is how you watch a running game from the inside. You set a breakpoint, the player pauses, and you read fields, step to the next line, or change a value and continue. A development build accepts a managed debugger. A release build is what you ship.
Example
You attach a managed debugger to a development build and set a breakpoint in TakeDamage. The game pauses on the hit. You read the health field, step over the subtraction, and continue. Pausing on machine code instead needs a native debugger.