By necessity, there will be distinct elements, and... case-by-case, shared elements. You decide how alike or different they are.
Think of it as two apps inside one, where Apple has done it's best to do some of the work for you when creating a new project/app.
My suggestion is to move from wrestling with concepts, to actually working with just such an application. Do this by creating a new project in Xcode, selecting an iOS template, such as Master-Detail (choose 'Single View' for the most basic example if you want really simple at this stage). A Universal app will be generated by default. Note the setting in General>Deployment Info>Devices... Universal.
Select main.storyboard, and choose from iPhones and iPads at the bottom of the editor window to see the different 'View as...' screen size choices. Set zoom so you can see the entire contents, then switch back and forth between iPhone and iPad to observe.
The UI will be sparse, but the designs and under-the-hood elements for each should be obviously distinct. Add new UI elements to each and see how they perform differently in the simulators. Notice you can make them as similar or unique as you wish.
Again, when a Universal app isn't used when it should be, App Review may pushback. Making an iPhone-only app first, as an example, then deciding to also support iPad later is a common dev mistake. Your users will thank you when they have both devices and they only need to interact with one app.
Finally, being able to maintain one app instead of two reduces the long term work faced by the dev.
