combustion and burning

I think you have a fundamental misconception in "logic" or meanings of English.

Burning is "a form" of combustion means there are many types of "Combustion" and buring is only one type of combusion.

"Combustion" is a gas-reaction is a physical description of a process. It is not to define the "materials of the combustion.

It is true that combustion is gas-reaction...but the source of the "gas" or gaseous reaction can be:

solid reaction with gas - wood burning is a combustion of reaction of wood(carbon) with air (oxygen) to form CO2 (gas) and heat.

gas reaction with gas - natural/town gas burning on stove is CH4 + O2 = CO2 + heat!

liquid reaction wtih gas - oil burning is vaporization of the oil and react with air (oxygen)...

All these are combustions: gas-phase reaction means the "micro" process of the combustion is reaction between the air(gas) with the gasous molecule of the "material" burning.

Of course this is a simplified expanation, not a text book definition. But from a simple sense, burning is what you can see; combustion may refers to the molecular level of the reaction.

The burning of potassium occurs in the gas phase. Note that the flame is above the potassium (i.e. gas phase), and the lilac colour of the flame is caused by the gaseous potassium ions.