At 5:41 and 8:16, "Sodium Chloride belongs to the crystal lattice system" & "Calcite belongs to the rhombohedral crystal system".
It would be more appropriate to say that they crystallised as crystal lattices or rhombohedral crystals.
There are no systems as such that are named thus to which these compounds belong.
Jmol-Application Crystal-Structure-and-Unit-Cell 05-06 min 40-50 sec
Calcite is given as an example as under Rhombohedral/Trigonal Crystal Systems in NCERT Chemistry Text book 1, Chapter 1, The Solid State, page 8, Table 1.3
There are many other references that mention Calcite as Rhombohedral Crystal System.
Alternative Title: rhombohedral system
Trigonal system, also called rhombohedral system, one of the structural categories to which crystalline solids can be assigned. The trigonal system is sometimes considered to be a subdivision of the hexagonal system.
This tutorial is mainly aimed for high school students/school teachers, so we refer to examples from NCERT text books.
These tutorials are not aimed at teaching the subject in detail, they are only aimed to explain the software interface and how to use the features available.