An APP in this context is an application related to blockchain. A DApp is a decentralized application. All DApps are apps but not all apps are DApps.
If the governance system of an application is decentralized, then it is called a DApp. An interface (I assume in this context you are referring to a blockchain interface) is an application used to interact with the blockchain.
For example, Steemit.com is a blockchain interface for the Steem blockchain because it allows general users to interact with the blockchain.
Blockchain interface applications can be decentralized or centralized. For example, Steemit.com is a centralized blockchain interface since it is controlled by a single entity.
Steemit.com is controlled by Steem Inc, a USA based company that created the Steem blockchain.
Steem.io the main software that runs Steem is decentralized because it isn't controlled by a single entity or it doesn't have a single point of failure.
General blockchain applications are either client based interfaces (e.g. vessel) or centralized applications.
Then there are DApps such as Musing, DTube etc. Though the musing website is centralized, the underlying back end of musing / DTube is decentralized. Both use Steem api nodes to fetch content from the blockchain.
The last time I checked, there was 10 running api nodes. So, even if one goes down, musing / Dtube can migrate / change to another. That's why these apps are called DApps.
Good friend, I will try to answer you simply, an interface is that it allows you to interact with the string of blocks of steemit, i.e., can do exactly the same thing you do in steemit.
On the other hand, an application and a dapp when we talk about steemit has been the same thing.
It is an application built on an existing as bitcoin or ethereum string of blocks, in this case you're referring to steemit.
It has its own chain of blocks, which means that all of the applications built in this chain of blocks are dapps.
On the other hand, there are in steemit dapp which offers any service or feature that steemit do not possess. How to upload music, in the case of Dsound, or upload videos for tube Dtube.