Bad options are bad.
Automatic could mean a number of things, but would generally refer to a "hydramatic" style transmission which operates on hydraulics, uses a fluid coupling (typically a torque converter) in place of a mechanical clutch to engage the transmission.
Manual would most typically be a "synchromesh" type transmission which uses a synchronized gear box where the appropriate gear is manually selected, typically by a "stick" and is engaged via a mechanical clutch.
But this is where your options come flying off the rails.
"Paddle shifting" usually refers to a Manual Sequential Transmission (which uses a manual gearbox which unlike a synchromesh transmission can be shifted without use of a clutch pedal (except for standing starts), however the gears have to be cycled through in order.
It could also refer to an "Automatic Sequential Transmission." Which is basically a dumb gimmick which is a typical hydraulic automatic transmission that affords the user the ability to manually select gear shifts in sequence, which has very little practical application save for driving on steep terrain (although most automatic transmissions have a "low" option already which would achieve the same effect.) But a "Manual automatic" could also use "paddle shifters".
But you also left out electronically controlled automatic synchromesh transmissions; which use a typical mechanical transmission design but feature electronic controls that automatically cycle through the gears in a logical order but still operate on the same mechanical principals as a "manual transmission." These are becoming increasingly popular in commercial vehicles because they have all the awesome longevity and fuel economy of a typical manual transmission while affording the driver the extra attention span to not be worrying about shifting gears.
There is also the "continuously variable" transmission (or CVT) which for all intents and purposes is an automatic transmission, however, rather than cycling through a set of fixed gear ratios the gear ratio actually continuously changes (there are a number of different technologies one might use so I won't get into details). Typically a CVT leads to better fuel economy because the engine, in typical driving conditions, is constantly running at its most efficient possible RPM (save for hard acceleration).
Then, not common in any practical application save for the drag strip you have the direct drive transmission; which has no "Gears" in the conventional sense, the engine gets engaged directly to the drive mechanism and by leaving out the middle man so to speak it ensures maximum power delivery to the wheels. Commonly used in applications where maximum power to the wheels is desired, and where the power involved is so great it would absolutely destroy any conventional form of transmission, I.e. top fuel drag racing.