To answer your question, both of them can be used for the creation process. All you have to do is ask “what are you performing the action upon?” to differentiate what you should be using. Let us assume that what you're designing an API for, is for asking questions. If you want to use POST, then you would do that to a list of questions. If you want to use PUT, then you would do that to a particular question.
Do you name the URL objects you create explicitly, or let the server decide? If you name them then use PUT. If you let the server decide then use POST.
PUT is defined to assume idempotency, so if you PUT an object twice, it should have no additional effect. This is a nice property, so I would use PUT when possible. Just make sure that the PUT-idempotency actually is implemented correctly in the server.
You can update or create a resource with PUT with the same object URL
With POST you can have 2 requests coming in at the same time making modifications to a URL, and they may update different parts of the object.
Used to modify and update a resource
POST /questions/<existing_question> HTTP/1.1
Note that the following is an error:
POST /questions/<new_question> HTTP/1.1 Host: www.example.com/
If the URL is not yet created, you should not be using POST to create it while specifying the name. This should result in a 'resource not found' error because <new_question> does not exist yet. You should PUT the <new_question> resource on the server first.
You could though do something like this to create a resources using POST:
POST /questions HTTP/1.1
Note that in this case the resource name is not specified, the new objects URL path would be returned to you.
Used to create a resource, or overwrite it. While you specify the resource's new URL.
For a new resource:
PUT /questions/<new_question> HTTP/1.1
To overwrite an existing resource:
PUT /questions/<existing_question> HTTP/1.1