Lets keep this topic to one tool, start others for other tools. Although shaping and manipulating tools could be a single topic.
I'm not sure that this would be such a good idea. In fact the topic is already about four terms: pontil and parison, blowing iron and bulls-eye, which is how you began it!!
Starting a new topic every time someone mentions a separate point of reference is going to be much more confusing.
According to Allan Scott, the glass making tools called 'Pucellas' - sometimes known as Jacks - have always been called 'Priscillas' at Caithness! In fact, in the Caithness millefiori paperweight 'The Glassmaker', which shows the glassmakers' tools in picture canes, the description card actually refers to these as 'Priscillas'!
So far as I can see, Leni is making a very important point that links in to her earlier comment. Normally, there would have been no need to write down names of tools in a working environment. So names would not have been recorded in writing but would have been mainly been passed on verbally. When language differences came into play with migrating glassmakers bringing their own terminology, it would have been open season for mix-ups!
Hence, pontil (old french for bridge - the bridge being the bridge of glass between the iron and the base of the vessel) became punty (puntee)*. Forcella (forcelli) [Italian for Fork (s)] became Pucellas** and then became Priscillas. Marbre (French) became Marver. It is only at a later date, when researchers want to record the names of tools that these adulterations come to light.
As to Parison, I have always understood that this was, as Adam D says, the first forming stage, ie a blocked, or papered, or paddled, roughly oval shape on the end of the iron with some air introduced. I believe that the word "Parison" is also adulterated from (hugenot) French and comes from the verb "apparaitre" to appear - present participle "apparaissant" The context being the appearance of the bubble at first blowing. It could also come from "paraitre" pp "paraissant".
I don't know why jacks are called jacks, but it would not have been a big step for the translation of Forcelli - Forks to become Jacks.
*except that I have a vague memory of Ivo disproving this theory some time ago!
**only recently learnt that pucellas are an adulteration of forcelli