Vario, short for variometer, is usually used in English
AFAIK only in gliding terminology. Our glider varios are sensitive to small changes in vertical velocity. The equivalent instrument in powered aircraft, from small single engine to airliners, is usually called a VSI (again,
AFAIK) – Vertical Speed Indicator.
I suspect the same term for both is used in France – vario. If my surmise is correct, we have a translation from French to English of “vario” to “vario”, whereas it would be more usual to translate vario as VSI.
Hope that helps. If I have it wrong, and English usage in airliners is to call it a vario after all, I shall stand corrected (and have learnt something!).