What you are doing first is called variable interpolation or string interpolation. You can read more about it here, on PHP docs and here, on Wiki.
It's a feature in PHP that allows you to pass a string and have variables/placeholders inside interpreted.
In your second example you are using single quotes, which does not provide this feature, so you will have to break it up and add the variable manually to the string:
return redirect('/cards/' . $note->id);
If you are interested in a more elaborate explanation and the performance behind it then you can read more on this answer here by Blizz
He concludes that:
Everyone who did the test concluded that using single quotes is marginally better performance wise. In the end single quotes result in just a concatenation while double quotes forces the interpreter to parse the complete string for variables.
However the added load in doing that is so small for the last versions of PHP that most of the time the conclusion is that it doesn't really matter.