Dry cough -

...The Hering-Breuer reflex itself does not initiate a cough, but it does have the effect of strengthening a cough.
[Wet cough and dry cough]
Clinically, coughs are divided into those that are accompanied by phlegm and those that are not; the former is called a wet cough, and the latter a dry cough, or what is commonly called a dry cough. Wet coughs are seen in diseases that produce phlegm, such as chronic bronchitis and bronchiectasis.

*Some of the terminology explanations that mention "dry cough" are listed below.

Source | Heibonsha World Encyclopedia 2nd Edition | Information

…ヘーリング=ブロイエル反射自体は，咳を始動するものではないが，咳を強めるはたらきがある。
［湿性咳嗽と乾性咳嗽］
　咳は臨床上，痰を伴うものと伴わないものにわけられ，前者は湿性咳嗽，後者は乾性咳嗽いわゆる空咳とよばれる。湿性咳嗽は，慢性気管支炎や気管支拡張症など痰の出る病気にみられる。…

※「乾性咳嗽」について言及している用語解説の一部を掲載しています。

出典｜株式会社平凡社世界大百科事典 第２版について | 情報