I have read on the internet that the horn serves to improve the coupling efficiency between the speaker driver and the air. ... The main advantage of horn loudspeakers is they are more efficient; they can typically produce approximately 10 times (10 dB) more sound power than a cone speaker from a given amplifier output. Higher SPL with less power compression means a more dynamic delivery. Horn mids that work to 300Hz are HUGE. Horns can tend to have a cupped sound when improperly designed. Typically there is greater nonlinearity in the frequency response of a horn compared to a simple cone driver. Those are some of the objective differences. Subjectively, I've heard great horn speakers but I've heard better nonhorn speakers when critical listening at normal volumes is the objective.
There is one other major difference between horns and cone/dome that hasn't been mentioned yet. Horns have a rising on axis (polar) response but maintain a constant power (off-axis) response. Cone/dome has a more constant on-axis response but a falling power response. Cone/dome will sound better on-axis while sitting in the "sweet spot." Horns will sound better in a large or open venue simply because of their better power response.
What is the difference between horn & cone? Is it just the shape?
Both drawing have the same cross sectional area.
If you look at outside concert speakers they are often wooden cabinets with 16 or more square shape wooden horns in the cabinets. Bottom of each horn appears to have a small square speaker.
A horn is really a streamlined speaker it should be much more efficient than a cone.