ModelBuilder & Its Exported Python Script

I tested ModelBuilder and Python scripts in such 2 scenarios. The results are posted below. Hopefully you can help me for some questions.
Scenario One: No parameter in ModelBuilder
1) Run the ModelBuilder - Successful.
2) Run the script exported from the ModelBuilder in PythinWin - Successful.
3) Run the Script tool that sources from the python script in 2) in Catalog - Successful.
Scenario Two: With parameter in ModelBuilder
1) Run the ModelBuilder - Successful.
2) Run the script exported from the ModelBuilder in PythinWin - Failed and no parameter input boxes.
3) Run the Script tool that sources from the python script in 2) in Catalog - Failed and no parameter input boxes.
The results impress me that
1) The scripts from the ModelBuilder with parameters do not work well.
2) To setup the parameters in python scripts, related python's syntax has to be used.
Is my understanding correct? Please feedback me your experience. Thanks.