The ‘Testpp’ node is the hda I create by press the Python Processor node's Save to Digital Asset button. These two nodes are all set as “Automatic” work item generation. But the Python Processor is static while the Testpp is dynamic by default.
I wonder why this happened, these two nodes are the same python script(almost), how PDG figure out which one is dynamic and which one is not?

A PDG node will automatically be set to dynamic if any of its inputs are a dynamic, or if it has a partitioner input that has dynamic work items in it. The reason for this is that if the input is dynamic, the processor can't generate off the work items in that input unless its also dynamic.

You can override the behavior usign the Work Item Generation parameter. If you set it to Static or Dynamic PDG will always use your selection. It's only when the parameter is set to Automatic that PDG will attempt to determine a selection on its own.

EDIT: If the test asset is indentical than that might be a bug with the badge. You can test that by dirtying your graph and doing Tasks -> Generate Static Work Items, to see if the test node is in fact generating static work items. I'll try to reproduce the behavior on my end