Both Debugger.Log and OutputDebugString have some key similarities:

  1. The both log string for debugging purposes
  2. Both have thread-affinity. (The debugger can find out which thread logged)
  3. Data is piped through with no additional semantics in the debugger pipeline.

But they have some key differences.

  mscorlib!System.Diagnostics.Debugger.Log kernel32!OutputDebugString
Managed? Managed Native
Debug events: Managed debug event, see here for how debugger retreives it.   Native debug event. Retrieved via a OUTPUT_DEBUG_STRING_INFO event
Information that's logged  (level, category string, message string) (message string)
Activation Can be enabled / disabled (enabled from debugger via ICorDebugProcess::EnableLogMessages, and can be checked via  Debugger.IsLogging). Debugger must enable to get the messages. Always enabled
misc Calls OutputDebugString with category and message strings.  
Sniffing outside a debugger Must be attached as a managed debugger to get the managed log events. (DbMon can still sniff the OutputDebugStrings) Events can be sniffed from DbMon even when a debugger is not attached.

If you're writing managed code, you should probably call Debugger.Log() instead of pinvoke out to OutputDebugString.