I have read that there is a difference between OneNote and OneNote 2016 (and 2010, 2013, etc.), and in the lightweight version, it seems I cannot insert equations, customize the layout, etc.
Existe de fato uma diferença:
Qual é a diferença entre o OneNote e o OneNote 2016
How can I install OneNote 2016? If I go to www.onenote.com to install the full version, it says that OneNote was already shipped with Windows 10.
Você pode baixar o OneNote 2016 em aqui , apesar do que o site diz, você é eventualmente enviado para o download do executável.
Faça o download do OneNote 2016