Infinitive or Gerund after verbs?

[Nola]

Hello everybody
Could anybody kindly tell me the difference in the meaning between using the gerund or the infinitive form of the verbs after such a verb like "begin" or many other verbs?

e.g
We will continue to explore the cave next week.
We will continue exploring the cave next week.

She started to shake.
She started shaking.

He began to speak.
He began speaking.

(offer - promise - decide - want - agree - refuse) Those verbs are mostly known to be followed by infinitive verbs
(imagine - stop - pretend - suggest - enjoy) Those verbs are mostly known to be followed by gerund (v.+ing)

Many great thanks,
Nola

[Mister Micawber]

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There is no substantive difference in your 3 pairs of sentences.

Others have different meanings, e.g.: 'stop to do X' = 'stop doing Y in order to do X'.
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Native English teacher at Mister Micawber's

[Nola]

Hello Mister Micawber,
Thank you for your reply. I've just learnt that there's no difference in meaning between such sentences. Which means that there are some verbs that can be followed by both infinitives and gerunds with no difference in meaning (e.g. continue, start, begin, love ...etc). But in using other verbs like (stop, try, remember, forget...etc), we can find a big difference in meaning between the usage of the infinitives or the gerunds after them.
The question is:
What about verbs like (suggest)? I've just learnt that it should only be followed by a gerund, but I found other cases to the same verb referring to the infinitives.
e.g. She suggested going to the party.
She suggested to stay close together.
What is the difference between such sentences?

Thanks,
Nola

[Mister Micawber]

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No difference in meaning, but I think you will find many grammarians that consider 'suggest + infinitive' substandard.
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Native English teacher at Mister Micawber's