With instruments such as violins or trombones, it is possible to shift from one tone to another fluidly. What is this practice called? When has it first appeared in [Western] music?
Sliding between two notes, up or down, and including the notes 'in the cracks' at the same time, is called portamento. It's been around for as long as the particular instruments it's possible to play it on. As you say, trombones, unfretted stringed instruments. It's possible also on trumpets and clarinets, easier to play in the upper registers.Slide guitar works well, but it's impossible on acoustic pianos - although a lot of keyboards - synths - have a portamento setting.
Glissando is not an Italian word, unlike so many other musical terms! It's a bastardisation of the French 'glisse' - to slide. It tends to be kept for instruments on which slides can be performed - catching as many notes in between start and finish as possible - but none really 'in the cracks'. In fact, harps and pianos are most considered with reference to the term 'glissando' - on piano, it's more usual to gliss on the white keys - so it's not even a chromatic episode. Trombones are difficult to perform a proper glissandos (glissandi?) on, as once past the end of the slide motion, a new embouchure needs to be made.
When has it first appeared in [Western] music?
"Portamento [has been] considered an essential aspect of good singing for hundreds of years..."
-- J. Potter, 2006, "The rise and fall of portamento in singing", Music & Letters 87(4), p. 523
Glissando is a metered slide from one note to another that takes the given duration of the first note to perform. On instruments like a piano it is usually approximated "discretely" by sweeping across the white or black keys. Portamento is an unmetered smooth jump "between" successive notes (in timing similar to grace notes) like what happens naturally when having two different slur-connected notes played by the same finger on the same string of a violin and separated by a position change. There is no way to approximate that on a keyboard instrument.