Let's say I have a spell, and multiple versions of the same spell, different only in one aspect.
Creo Ignem: Hot Flame lvl 5
Hotter Flame lvl 10
Hottest Flame lvl 15
They are identical, except in heat (damage).
When I cast them, do the incantations sound the same? Same gestures? Is there anything to tell them apart, other than the heat?
If casting a spell was the same as invoking a computer program from a command line, I imagine the 3 spells would be something like:
exec CrIg /level=5 /file="Hot Flame" /args=x:y:z
exec CrIg /level=10 /file="Hotter Flame" /args=x:y:z
exec CrIg /level=15 /file="Hottest Flame" /args=x:y:z
So in my view, large portions of the incantations/gestures will be the same, representing it is a Creo Ignem spell, but certain specific components are unique to the specific spell.
Assuming the invocation was essentially uttering a phrase along with a gesture I would expect the variation to be a change in a single word, and probably not a profound one - think of it like coffee orders at Starbuck's- if you don't know a vente from a grande it all sounds the same. Maybe one finger is held in a different position as well.
I would expect the incantations and gestures to be very similar but not identical. There's an extent to which all spells of a given form and technique combination are similar, otherwise you couldn't recognise spells to counter them by fast-casting, but the similarity should be stronger than that. The incantation might have extra qualifying phrases or just repeat some words, the gestures might be more emphatic, that sort of thing.
You might want to take inspiration from how British Sign Language handles intensifiers (I suspect ASL is similar but I don't know it). There is no separate sign for "very", you use your face and body to act out the emphasis. For example, the sign for "hot" looks like wiping the sweat off your brow. To sign "very hot", you make the same gesture but also slump and pant as if you were physically overheating.
I would suggest that there are subtle but pervasive differences. Like text in a different size and font; still recognizable but nothing as simple as changing one word or gesture, or as uniform as making the gestures a little wider. In contrast, Ranges, Durations, and Targets are relatively localized and don't effect the whole spell; changing the range from touch to voice would keep the same size and font, but clearly change a few particular words or gestures.
I base this off virtues such as Flexible Formulaic Magic and Mutantes vis Boosting being able to alter the Range, Duration, and Target but not able to increase the guideline form +6 damage to +9 damage.
It depends. I suspect magic is a very personal experience in that regards. A caster designing several versions of a spell might very well use the same word, but different casters might not. Ward against Beast of Legends, for example, says that "When a magus is making this and most other wards, a common gesture employed is the Fig Sign." This leads me to say that using the Fig Sign is a common gesture, probably learned through magic theory, but that there are alternatives, which other magi might use instead (and yet they are common enough that you know which Form they are related to when using a fast-cast defense). And so on with the words. After all, if being silent is merely a penalty, then most likely the words you choose to use are optional too.