You need to check which form can go with which verb.

"Like" can take either infinitive or gerund. "Dislike" can only take a gerund.

Both "like to play" and "like playing" express the enjoyment of something, but there is a subtle difference: "like to play" means whenever it's possible; you enjoy the idea. "Like playing" is part of your regular lifestyle; you enjoy the habit.

Your teacher is correct: both sentences mean the same thing. English speakers use both interchangeably.

However, as you probably already guessed, the gerund and the infinitive forms don't always mean the same thing. The general rule of thumb is that we use gerunds when an action is real or complete, and we use infinitives when the action is unreal or has yet to happen. For example:

1a) I stopped smoking. This could mean I quit smoking or I stopped smoking for the moment. Either way, it happened already.

1b) I stopped to smoke. This means I stopped doing what I was doing in order to smoke. This action has yet to happen.

That being said, we cannot simply replace a gerund with an infinitive (and vice-versa) wherever they appear. Sometimes, only one works. For example:

2a) We enjoy climbing mountains. This means we've probably experienced climbing mountains before and we liked the experience.

2b) We enjoy to climb mountains. This is incorrect because it makes absolutely no sense. How can we enjoy something if it hasn't happened yet?

I hope this helps. Please let me know if you have any more questions.

Hallo Riku ,

Yes , Two sentence are the same . You can do that with verbs as :( like) but not all the verbs .I wll give you some examples .

Verbs like   stop _ get used to _ interested in _ objects to _ be worth     the verb after them should take ing for ex : I stopped smoking 

You can't say I stopped to smoke 

I get used to living here     you can't say I get used to live here 

There are other verbs just in infinitiv form so you can Google it 

I hope that would help you