If you're referring to a key on your keyboard, it can't be both Backspace and Delete, because these are two different actions. Backspace deletes the character before the cursor, while Delete deletes the character after the cursor.
On some keyboards, the same key might be used for both functions (it is on mine). Pressing the key invokes Backspace and removes the character to the left of the cursor. If I hold the Function (Fn) key down and press the DEL key, the character to the right of the cursor is deleted.
It sounds as if you might be pressing Shift or Control together with the DEL key. This will in some configurations remove more than a single character, e.g. a whole word. Check the documentation for your keyboard to find out how to operate your DEL key.