Differences in view about the chakras
There seem to be lots of differences in which properties are attributed to chakras by various authors. Also the names of the chakras differ a lot.
The names of the chakras
The second chakra, here called the Sacral chakra, is sometimes called the Spleen chakra. This practice seems to originate in C.W. Leadbeater's book The Chakras (which was the first book to introduce the chakras in the West). However, Leadbeater is quite explicit that the Sacral chakra (the Indian Svadhisthana chakra) is different from the Spleen chakra he discusses. He even considers opening the Sacral chakra to be disastrous.
Leadbeater's description of the Spleen chakra bears some resemblance to the functions of the Spleen from Chinese Medicine (belonging to the Spleen meridian). It is supposed to deal with transporting energy throughout the body. It doesn't seem to have anything in common with the spleen from Western medicine, which purifies blood, however Leadbeater situates the Spleen chakra at the spleen.
So it has to be concluded that it is incorrect to call the Sacral chakra "Spleen chakra."
The functions of the third chakra, the Navel chakra, are closely related to the functions of the Liver and Gallbladder from Chinese Medicine. It's about assertiveness and decision making. Many people have come to call it the Solar Plexus chakra. The function of the Solar Plexus, distributing nerve signals, just doesn't have anything to do with the functions of the Navel chakra.
The location of this chakra is not at the Solar Plexus, but also not at the navel. Actually it's somewhere in between, and not at the front of the body, but near the spine. Here the name Navel chakra is preferred, because it's more neutral than Solar Plexus chakra, and it doesn't suggest a function that isn't there in this chakra.
It may be that people like the name "Solar Plexus chakra" as it suggests the associated color for this chakra, being yellow.
Functions of the chakras
Particularly the Crown chakra seems to be subject to idealization by various sources. It is supposed to be letting in only positive energy, help one knowing the unknown, and bring one into a state of bliss. This seems to ignore that there may be negative aspects about this chakra (e.g. when it is in an excessive state).
Bliss isn't really a state, it's an emotional reaction to a state. I doubt that that state will be the result of just one chakra being opened, it is much more likely that a balanced and open state of all chakras would result in feelings of bliss.
Location of the chakras
There are quite some differences in where each chakra is supposed to be located. The differences are in what level in the body they are supposed to be and whether they are at the front or the back of the body.
Often the chakras are depicted to be situated in the front of the body, particularly on many beautiful pictures, but just as much on the spine. Authors that situate them in the front, or somewhere halfway in the body, often do depict a connection with the spine. Almost everyone seems to agree that the chakras lie on the midline of the body (although there are some exceptions).
The first chakra is by many authors situated between the anus and the genitals. But there are also authors that locate it at the lowest part of the spine (e.g. Leadbeater).
The second chakra is usually located at the sacral bone, but some locate it at the genitals. As discussed above, some confuse it with the Spleen chakra (which is not in the Indian chakra system) which is situated at the spleen (in the lower ribcage, left of the center).
The location of the third chakra differs with every author, or so it seems. Some locate it about half a handwidth below the navel, inside of the body. This is the same spot as the Dan Tien from Chinese Medicine and martial arts, so here it seems these two energy centers are supposed to be the same thing. Others locate it in the back of the body, slightly above the navel. Then many think it's situated at the Solar Plexus, which is just under the breast bone, two handwidths above the navel, on the front of the body. And there are also authors that situate it spot on the navel.
The Heart chakra is mostly considered to be located at the center of the chest, however Leadbeater situates it in front of the heart, so left of the center.
Most authors agree about the location of the next two chakras, the Throat and Third Eye chakra. The Throat chakra at the base of the throat and the Third Eye chakra between the brows.
The Crown chakra, is by some considered to be on the highest point of the head, others consider it to be above the head, so not in the body at all.
What to do with these differences?
The question is whether these differences matter.
The differences in naming seem to be the least of the problems, although these seem to be pertaining to different locations as well.
Although the differences in location at first sight don't seem to matter much as well, this is not the case. Many techniques to open chakras depend on concentrating on the spot where the chakra is situated. So concentrating on the wrong spot makes the technique less effective. The more accurate the locations are known, the better.
It would be good if it was clear what functions the chakras have. But unfortunately there is quite some difference of opinion. Knowledge like this has to come from observation of people or self and there are many disturbing factors.