You are right. Some journals are purely subscription based while others are purely OA. This is generally mentioned somewhere on the journal website. An additional point that will help you figure out which model of publication the journal follows is to have a look at the mode of payment. Traditional subscription based journals commonly charge per page and per color figure. However, OA journals typically have just a flat article processing charge and do not charge per page or per figure. So, if the journal mentions an article processing charge, you can make out that it is an OA journal, and if per page charges are mentioned, you can understand that it is a subscription journal.
I confirmed the difference of the OA model and the subscription model in an article on Editage Insights. According to the article, most of journals provide both options, but I think some journals accept only one of them. Is the any point or keyword to distinguish that?