Spanish gerundio: conjugation/form of a verb (ending -ndo) that shows an action in progress (without being specific). In general:

-ar verbs → stem + -ando

-er and -ir verbs → stem + -iendo

Estoy buscando – I’m looking for (compound verb)

Salío corriendo – He went out (left) running (used as an adverb)

In general, the progressive/continuous tenses are:

estar + gerundio

e.g.,

Él estaba leyendo – He was reading (imperfect)

Estoy leyendo – I am reading (present)

Estuve leyendo – I was reading (past – not actually progressive/continuous)

Estará trabajando – He will be working (future)

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In English

• the gerund is the noun form of a verb, ending in -ing, as in: Swimming is fun. This use, in Spanish, uses the infinitive of the verb: Es divertido nadar.

• the present participle is the -ing form used in compound verbs: I’m swimming (Estoy nadando).

Hence gerundio best matches present participle