Optical sizes are types of font styles that have been adapted for different text sizes and are available separately. It is not uniform which subdivisions there are. There is a variant for reading texts (known as text, regular, text set, for example) and an editor that is optimized for very small text sizes (known as a caption, for example).
Display fonts are not automatically screen fonts. “Display” is a term for fonts for large sizes (English “to display”, to display). They usually have finer details, a higher line contrast and are narrower.
The font “Legilux Serif Display” (above) compared to the “Legilux Serif Text” (below). The “Display” variant is the right choice for big headlines.
Helvetica Now Micro (left) compared to Helvetica Now text (right). The Micro variant is adapted for small font sizes.