Singleplayer generally refers to the Freelancer compaign, whereas Open Singleplayer is basically just the multiplayer world without other people.
When you finish the campaign, it allows you to play on in this ‘Open Singleplayer’ mode, where are there no set objectives. Basically like a sandbox mode. This is identical to vanilla multiplayer.
Many mods make changes to the game that breaks the Singleplayer campaign, so generally they either disable singleplayer completely, or disable the campaign and make it open singleplayer right from the start.
Hope that helps. 😄