I would recommend that you read the works by Nelson Cowan regarding short-term memory, long-term memory and working memory to get a clearer picture on this topic.
You may want to read his paper What are the differences between long-term, short-term, and working memory? Prog Brain Res. 2008;169: 323–338. doi:10.1016/S0079-6123(07)00020-9.
Atkinson & Shiffrin tried to create a model of memory functioning, while the model by Baddeley and Hitch is more focused on one specific aspect of short-term memory. In my clinical and research practice, the Levels of Processing model by Craik & Lochart is more useful than the one by Atkinson & Shiffrin. For example, you might expect that a patient with Alzheimer's disease recall more words from a list if presented with a semantic category (Free and Cued Selective Reminding Test) than if presented auditorily (Rey auditory Verbal Learning Test), even if words from both lists are temporarily stored the same amount of time in the A&S short-term store. This can be later used for intervention (e.g., repetition within the short-term store is not a good way to teach patients with AD verbal material, definitely not better than deep processing).