When latticino is like this, do we call it muslin?
Possibly. However, this Fratelli Toso version is not as fine as in many of the antique French weights, which defintely gave an appearance of a fine lacy ground. When the latticino is a bit "chunky" I prefer the term "a bed (or ground) of latticino". "Muslin" ground weights are also called "Upset Muslin".
I'm not sure of the origin, or whether it was a collector or a factory term, but it was certainly used in old auction catalogues from the mid-20th century.
Latticino seems Italian based (Latin) for lattice work?.
Latticino (or latticinio) is Italian for white, or milk, glass. It's the white of the twists that gives rise to the use of the word for these pieces. Also note that "filigree" is just an English translation of the Italian "filigrana" which actually covers both white and coloured twists.