'Like' can be followed by either a gerund or the infinitive with 'to'. They are both grammatically correct. In some cases, they may be interchangeable; in other cases, there is a subtle difference. My impression is that the gerund is more common in British English, while the infinitive is more typical of American English. Let me tell you about the first time I came across an instance of 'I like to V'. One day, when I was a student, I remember seeing an amusing American cartoon. It depicted a suburban home, with a rather plain young woman sitting in an armchair opposite a guest, a young man of a similar age, sitting in a second armchair. Behind this second armchair, unseen by the young man, stood a desperate-looking middle-aged dad, holding up a handwritten notice prompting the daughter to say "I like to cook". This struck me as an unusual construction, as I had grown up speaking British English and was accustomed to always hearing and saying "I like Ving". I had never encountered "I like.." with an infinitive before, used in the sense of "I enjoy doing this". That was a long time ago, and the lines between AmE and BrE are more blurred, and you will come across both forms being used everywhere. But there is still a difference, at least for some BrE speakers: When I say "I like [doing something]", this refers to the fact that I enjoy the activity itself: it's something that I find enjoyable. When I say "I like [ to do something]", this can mean that I think that it is a good thing to do, even though it isn't enjoyable. We often use this for routines. For example, if you say "I always like to wash the dishes before I go to work in the morning" or "I like to have a dental check-up every four months". Here, we're obviously not saying that these are fun activities: we're saying that they're wise practices or good habits which we like to keep.

There are strict, but fortunately relatively easy to follow, rules for the use of the English verb tenses. E.g. see them here: - https://grammar.cl/Notes/Present_Tense_Progressive_Tense.htm Cheers!

Hi. They are the same and grammatically correct. You can use any of them in whatever context.