I did a bit of googling and it seems that yes, inserting paragraphs rather than linebreaks is the default behaviour of TinyMCE which leads to the appearance of double spaces. As I mentioned before you can use shift+enter to make a linebreak instead. It looks like there are a number of different tweaks that one could make to the TinyMCE config (not a user editable thing) that can produce either the single line behaviour or give the appearance of single lines but I'm guessing changes here might mess up what you would expect to see when you swap editors.
In the short term I think you either need to adapt to using shift+return for single lines and just return for paragraphs or switch to the markdown editor instead (which is even more like the richtext editor now thanks to the Rich Markdown plugin.