Hello,
Like I said, the data for all these systems is pulled from the same source.
I imagine your issue stems from the player you use. In order to display slides, a player with that plugin must be used.
In KMC, when you go to the preview and embed form, you can choose the player you wish to use. Select the same one you use in KMS and it should work correctly. In Drupal, you also define the uiconf ID for the player you wish to display, likewise, that player should be one that supports displaying slides.
Hope that explains it.