A tautogram (Greek: tauto gramma, "same letter") is a text in which all words start with the same letter. Historically, tautograms were mostly poetical forms ([1]). The difference between a tautogram and alliteration is that tautograms are a written, visual phenomenon, whereas alliterations are a phonetic one. Most cases of alliteration are also tautograms, though certainly not all since different letters can frequently take on the same sound (e.g., circle segment or Catcher Ken). Similarly, most tautograms are also alliterations, although exceptions exist when using letters with multiple pronunciations (e.g., crazy child or pneumatic plate).
Veni, Vidi, Vici: a famous Latin sentence reportedly written by Julius Caesar
An example of a tautogram in Russian is a poem by V. Smirenskiy with all words starting with "L":
Ленивых лет легко ласканье,
Луга лиловые люблю,
Ловлю левкоев ликованье,
Легенды ломкие ловлю.
Лучистый лён любовно лепит
Лазурь ласкающих лесов.
Люблю лукавых лилий лепет,
Летящий ладан лепестков.