The difference between moshaf and Qur'an
1st you should know that the book you hold in your hand where the quranic text is in is a Moshaf مصحف. The Quran in first place refers to the orally transmitted text which content originally was kept as single "papers/pages" (quoted as the sahaba -may Allah be pleased with them- used everything "clean" they could write on like leather) by the moshaf writers or scribes among the sahaba.
Rather, the Qur'an is distinct verses [preserved] within the breasts of those who have been given knowledge. And none reject Our verses except the wrongdoers. (29:49)
So joining this single pages together made a Moshaf. This means that the Quran is the text inside the book not the book itself or what is between the book covers. Therefore it makes no difference between a text on a PC or a Smartphone, an ebook etc. when it comes to reading! As for the moshaf -the physical copy of the content of the Qur'an- there's a hadith saying:
no-one should touch the Qur'an unless he was pure. (al-Muwatta', Bulugh al-Maram)
Some scholars allow to read from a device without wudu', some even without tahara at all as mentioned in this fatwa.
As the device isn't regarded as a Quran or Mushaf! Therefore it's not meant by the verses(56:77-79):
Indeed, it is a noble Qur'an (77) In a Register (Book) well-protected;
(78) None touch it except the purified.(79)
But you should avoid reading Quran -from any of device or book- if you need tahara al-kubra (for example after having a physical relationship, menstruation etc. until you made ghusl) this is a literally interpretation of the Verses (56:77-79) but some scholars such as imam Shafi'i for example considered a Muslim is per se pure according to that only when ghusl is needed he will be considered not to touch a Moshaf! Or consider reading from a device as different from both reading from a moshaf or reading from the own memory... while the majority considers the later to need at least tahara al-Kubra ... (This sounds self-contradictory and inconsequent in my opinion)
As an advice: if you want to memorize Quran a hafidh told and recommended me to learn and read in this case always from the same book, as small differences in the books (layout, text color) somehow have influence on our memorization or memory!
Note there's also a common mistake many people do: reading Quran with the eyes only without moving the lips to pronounce the words most scholars say that by this you miss the thawab as you only look at the text and don't read it as we have been asked as good as possible
... and recite the Qur'an with measured recitation. (Surat al-Muzzammil (73:4))