While traditional Chinese practitioners consider there to be as many as 2,000 acupuncture points, the World Health Organization (WHO) identified 361 acupuncture points in a report developed in 1991. That being said, there is a smaller subset of points traditionally used by acupuncturists as many of these very important points have multiple actions in the body.
The second thing we need to address is the western idea of acupuncture as a monolithic system. There are actually multiple systems of acupuncture which have slightly different needling locations. Some of these recognized locations overlap and some locations are unique to a given system.
We also have so-called micro-systems, the most common being auricular acupuncture and Korean hand acupuncture. These systems map the entire body or parts of the body on to smaller areas like the ear or hand, and have an entire set of corresponding acupuncture points in these smaller spaces.
And finally we have so-called 'extra points'. These are locations with classically recognized function which often aren't located along any particular acupuncture channel.
All of the above makes it extremely difficult to pin down a concrete number of recognized needling locations. If we consider the classical channels (the channels most often taught in Chinese medical school) and the commonly accepted needle locations on those, we get roughly 362 points. Adding in the commonly taught 'extra points' gives roughly another 23 for a grand total of 385.
Lastly, the placement of needles does not 'fully depend' on recognized acupuncture points. There is a long tradition in Chinese medicine of 'ahshi' or 'ashi' points. These are locations on the body which do not necessarily correspond to a channel or a recognized needling location but which are sensitive to palpation (i.e. the location causes pain when pressed).
1. There are 362 points on the "regular" acupuncture channels. This would be what you would see on an acupuncture model or in a typical acupuncture poster. It is the points that are on the 12 "organ" channels and the midline front and midline back of body (Du and Ren Channel)
2. There are about 2,000 of what we call "extra points". These are points on the body that have been used and inputed into the system of "known" points. These points, however, are not necessarily "on the channel" per se or a part of the "channel points" in the charts.
3. There are also points on the body that are part of "microcosms" - that means that a certain body area can represent the whole body, such as the ear, the hand, the abdomen, the scalp, etc. These microcosms are a part of the Chinese medical idea that any part of the body can represent the whole - similar to how any piece of a hologram looks like the whole hologram. In modern speak, we can say that "every cell has the DNA of the whole body". So, each microcosm will have up to hundreds of points on them or will be "zones" where treating an area isn't so point specific as it is when using "channel points".
4. Chinese medicine and acupuncture in particular has many disciplines as different tribes/families or systems grew from the basic understanding. This is true of martial arts, cooking and other disciplines. With that said, there are some systems that also have points that are a mix of "extra points" and "microcosms" that may or may not be listed in the above categories - these would include what we can "Dr. Tung" style or some other family style. I do not know that number.
5. As acupuncture moved across the globe, other cultures have developed other systems - so the Japanese, the Koreans, the Vietnamese et al have also developed points they have found useful through basic theory, extra point theory, channel theory, organ theory, other microcosm theory or through empirical evidence. I do not know that number.
Because of all the answers above, ANY point on the body could potentially be an acupuncture point - one of the extra systems has what we call "ah shi" points, which are on the "muscular channel system". These would be similar to what some people call 'trigger points' or just 'knots' but it is more than just that. "Ah shi" points can appear anywhere there is a muscle.
So, yes, it is important to know what points you are using, but also know WHY you are using that point based on which system or discipline you are following. In a similar mindset, any wire pulled out of a power system will affect the electrical system, but how is it being rewired, removed, turned on/off, etc that will determine the result.
We have an adage: "Chinese medicine is easy to understand, but it is difficult to practice - Chinese medicine is easy to practice but it is difficult to understand" That circular thought is very real.