Both of those data points are from unverified, presumptive information. If I recall correctly, the "multiple puncture wounds" comes from an early local news story quoting an unnamed source, so probably a cop or medical worker speaking off the record about something he peripherally observed or something he heard (third hand information).
The data about her being shot is something that has been presumed working backward from FBI crime statistics, which record a gunshot homicide for that county that has dates that line up. That one not only relies on FBI violent crime data being entirely accurate (it's only intended to track trends) it also presumes there were no other gunshot homicides that went unreported in the county in that window.
Respectfully, all of that is not really accurate.
To start, you will find in the early threads on this case, where some in that town and very local contributed to this forum early on, here and there, and the word on the ground was she was shot. I live in a nearby small town and that wasn't wrong.
All of those who were there that day - campers, EMTs, LE, etc - would know cause of death, of course, as well as any with access to the autopsy, so it's not info that was truly unknown and murky. The general public just deliberately hasn't been told.
From the first day, LE was tight-lipped. The question was asked in a PC of how she was killed and whether she was shot and LE deflected from giving any answer to how she was killed.
The "puncture wounds" wording was not actually given by LE to the public, ever, but instead it emerged a few weeks later by a FOIA request where it appeared in a solitary SW. It never appeared again.
That turned the forum discussion on its head.
The FBI records were not discovered until a few years later, and with the prior perception being that she had been stabbed by something, there's been confusion ever since.
The fact that MB had to be the one in the FBI records is easy to know, as it's a small town, such incidents there are super rare (easily known by the community, and confirmed by LE's own words), and by the fact that all the records point to exactly 1 homicide of a female in her 40s in that city in 2016 -- which is transparently obvious to anyone who lives in the area. Every item within that FBI record points perfectly to the MB murder, and it is not one in a pile of many to try to figure out. Trying to make it into a mytery of who the records may be talking about, when none exists, is just a road to nowhere.
The question has been one of trying to align those two pieces of info, and there are two plausible explanations, and one that would seem possible but less likely -
1 One idea is that the bullet holes in MB that caused her death were called "puncture" wounds, as they technically would have punctured her skin, and LE was using obtuse wording in a searchable warrant to try to keep the details of her death away from the public. (It's a fact that LE was asked in multiple PCs about the details of MB's death, and each time either deferred to later, or just refused to answer at all. They have never told us anything.)
2 Another idea is that MB was killed by gunshot, but also received puncture wounds by some unknown weapon or item.
3 The less likely explanation is that FBI's records are botched OR the wording in the SW was a mistake, but dismissing inconvenient facts that emerge and are hard to understand as "mistakes" is usually an exercise that is a mistake in itself and only muddies what could otherwise be clearer.