Those are the basic differences, yup. Sora and 2300 both have the thumbshifter to shift to the smaller cog/chainring for right/left. As mentioned, this means you can't shift to a smaller cog/ring from the drops. If you only EVER stay on the hoods, then they're OK... but anybody serious about cycling wants to be in the drops for aerodynamic/performance reasons.

The Difference on the Tiagra is to shift to the smaller cog or chainring you use a lever tucked in with the brake lever that you can use either from the hoods OR from the drops. This follows the same design as Shimano's higher-end road groups.

Also, 2300 is eight speed, Sora is 9 speed. New Tiagra is 10 speed.