The difference between gerund and infinitive is an interesting problem. (Or possibly not an interesting one, but rather just an area of vagueness, where different people understand English in slightly different ways). The question what the difference between using gerund and infinitive after certain verbs is arises with a large number of English verbs, e.g. is there a difference in meaning between the first and the second sentence? And if so, is it the same difference for each verb?
- I like to read books. I like reading books
- I prefer to sleep late. I prefer sleeping late
- I hate to get up early. I hate getting up early
- She deserved to get a raise. She deserved getting a raise.
There was a lot of interest in this question around 1971, when an article called "Fact" was published by Kiparsky and Kiparsky. Not all verbs allow both infinitive and gerund. They noticed that with some verbs, the whole sentence entails that the complement (infinitive or gerund) is true, that is, if it is true that:
I regret arriving late it must be true that I arrived late, but if it’s true that I hoped to arrive on time then possibly I did arrive on time, possibly I didn’t. Then what the Kiparsky noticed was that verbs that entail that there complement is true (like regret), often can occur with the gerund but not the infinitive, i.e. in English you can’t say: I regret to have arrived late whereas verbs that don’t entail the complement (like "hope") often can occur with the infinitive but not the gerund: you don’t say in English: I hoped arriving late. They even claimed that some verbs had a difference in meaning depending on which of the two types of complements are used; their example was the verb "report", but I think earier example 4 is a clearer one: 4. She deserved to get a raise. She deserved getting a raise. That is, if the first is true, she may or may not have gotten the raise, but if the second is true, then she actually did get it. Or so they claimed. Not all English speakers find that the difference is as absolute as that, but most everybody takes (4b) as much more likely to be about an event that definitely did happen.Kiparsky claimed that this principle was pretty generally true of verbs in English that take infinitive or gerund complements, or both. But after linguists had checked a very large number of verbs, with a lot of different people, they found (a) lots of exceptions, (b) lots of verbs for which speakers of English disagree about whether there is an entailment of the complement or not. It’s true that there is a general *tendency* for gerund complements to refer to events that actually did happen (and even more so with derived noun complements, like "the detonation of a bomb near the airport by a terrorist"), and for infinitives to refer to events that may or may not happen (in the future, or may not have happened at the expected time in the past); finite clauses with _that_ ("The newspapers reported that a terrorist detonated a bomb") are somewhere in between on the whole, but are usually dependent on the particular verbs (compare previous sentence with "I regret that a terrorist detonated a bomb") But that is definitely not true for ALL verbs. The example of _like_ is more complicated because with this verb both kinds of sentences are about "generic events", or habits, not about a single event. It is (actually) true that I like reading books in German, even though I very rarely do read books in German; one linguist suggested that "I like my steaks rare" can be true even though I never get a rare steak when I order one, ever. So the question is not exactly whether a certain event did occur or may not have occurred (as with ‚report’, ‚regret’ examples above), since these sentences are not really about particular events so much as about your disposition toward certain kinds of events. Given this tendency it would not be surprising to discover that with _like_, there is some semantic distinction or other related to that difference, maybe only distantly. But also not surprising to discover there is no difference. There is one important difference, if you use the form "would like", then the sentence makes a statement about one and only one future event—that it will please me if it happens: "Someday I would like to see the site where the World Trade Center buildings stood." can be true if I definitely don’t want to see the site more than once. (It doesn’t rule out that I might like to do it more than one, but the sentence itself doesn’t say anything about that.)
This is not something that always happens systematically when you introduce "would", so (as I think you suspect) "would like to <verb>" is what’s called in linguistics an "idiom" (or "collocation"), by which is meant simply any phrase that has some meaning as a whole that goes beyond the literal meanings of the words in it. For example, "I would be happy to help you, if you need it" and "I am happy to help you, if you need it", the only clear difference is that the first is more indirect, hence (usually) more polite, or formal, but also maybe less of a commitment (as you also observed with _would_like_). As for myself, I can’t find any difference at all in meaning between "I like to read books" and "I like reading books" (when there is no "would" that is) —although I had to stop and think about this for a few moments to be sure. (Maybe I am a bit more likely to SAY the second if I do read books regularly, or if I’m commenting on an activity I’m engaged in at this moment, but that isn’t the same thing as a difference in what they MEAN.) But it would not surprise me at all if you take a survey and find that a significant number of people do find that there is a difference. But in that event, I would expect that many of them could not put their finger on just what the difference is, if you asked them to, and that of those who could explain a difference, it would not be the same difference for all of them. This could well be one of those cases (of which there are many, although they are rare in comparison to our vocabulary as a whole) where all the sentences using that word which we hear or read while growing up underdetermine the meaning of the word (or in this case, whether there is any difference between the two forms), so different people will make slightly different assumptions about the meaning, and in most cases never become aware that not everybody else shares their assumptions. ("I like to read a good book" is not a sentence I find completely well-formed semantically, so I would probably not say it, though I would not flinch if I heard someone else say it, and it should mean the same as "I like reading a good book", which is the same as "I like to read good books".)