"Back-End Testing" and "DB Testing" is the same term. In this we use to verify the DB with regard to the data which we submit though UI / getting delivered on the UI. Major entity around which the whole testing activity revolves is "Data". Some of the major (However not limited to) activities can be -

- Checking that the data is inserted into correct tables , fields/columns.

- Data displayed on UI reports can be verified by applying join queries.

- There are certain need which rather function from UI end also involve sending data onto some specific fields example

- there might be a requirement where in user asks to opt-in an agreement and on the backend in a DB table we are maintaining such record that which user opted for the contract.

In Another words:-

Back-end its a piece of the framework which is undetectable for client however give substance to front-end. Normally its a some API, which have information, yield, now and again db. In this way, from perspective of useful testing it is established black-box, or dark box in the event that you have entry to yield, as well as to DB and/or logs as well, or white-box in the event that you have entry to code. Contrast of back-end testing in non-utilitarian testing: load, continuance, recuperation, entrance, establishment, arrangement, incorporation.