Continue to + verb?

Why in the verb "continue to" when followed by another verb, this verb is written in its base form and translated as gerund (ending ing- in English and ando/endo in Spanish) despite the fact that it is preceded by "TO" [(continue to + verb in base form)in the writing ]= [(continue + verb in gerund) in the translation].

Solution 1:

In English both forms are possible.

Continue to walk until I tell you to stop!

Continue walking until I tell you to stop!

Unfortunately which to use depends on the context so I'm not sure how to give a rule. I'll think about it. Let's see if someone else gives an answer first.

Note that it is not "continue to" because the "to" does not belong to "continue". Instead it belongs to the following verb and indicates the infinitive form.

"Continue to walk." (incorrect)

"Continue to walk. (correct)