I know that some verbs oblige the following verb to take either the infinitive or present participle form, i.e.
- I will start doing this.
- I will continue to do this.
In these cases, the usage of the other form is apparently wrong:
- I will start to do this. WRONG
- I will continue doing this. WRONG
When it comes to mass usage, the Internet shows that people don't care too much about this, both forms being used in a quite equal proportion. How can I know which form is correct in a general case? If there is not a general rule, where can I find a list with the correct matches?
Do not believe everything you read in grammar books. There are many writers of grammar books ("mavens") who either invent spurious rules on English usage or over-prescribe out-dated or exaggerated "rules". In my opinion, there is no difference in sense or "correctness" between the infinitive and present participle forms in the sentences you quote. You will find few native speakers who would disagree, and who dictates usage of any language if not the majority of the native speakers?