The "to + infinitive" form and the -ing form (gerund) can have the exact same meaning: that the person speaking performs the action himself.  Therefore, "I like to swim" and "I like swimming" can mean the same thing:  that the speaker himself enjoys performing the act of swimming.  However, it is possible that the <em>gerund form</em> can have another meaning:  that someone else is performing the action.  It depends on the context.  Example:  "What sport do you like to watch?" -- "I like swimming."  [The speaker isn't saying that he himself enjoys swimming.  He is only saying that he likes to watch others do it.]   Another example:  A patient asks:  "Doctor, what type of exercise do you like your patients to do in order for them to lose weight?"  -- The doctor answers:  "I like running."  (This does not mean that the doctor himself runs.  It only means that the doctor recommends running in order to lose weight.  If the doctor had answered, "I like to run," it would tell us that he himselfs enjoys running; but it wouldn't directly answer the patient's question.")

they are different,

I like to swim means you suddently want to swim, not as a hobit

I like swimming means you like swimming all the time and you love for it is not temperary

Neil is Becky her answer correct? You should be able to answer that as a native speaker. I tend to agree with her. If a person would ask, 'what would you like to do next?', the answer, in my English language feeling, would sooner be: 'I like to swim!'. And not 'I like swimming'. But even better would be: 'I would like to go swimming'. Correct?

Hi Neil and Becky!

How are you?

I really appreciated your help.

Thank you.

Selma.