I've not been able to find a definition of the term "legal form" online, so I provide one here:
Definition:
The legal form of an organisation is the category into which it is classified by the law when determining how the members or member of the organisation relate to each other and to non-members.
This definition relies on the following elements:
To take the first three in turn: legal form is defined in relation to organisations: organisations have legal forms, as do a couple of degenerate cases such as bishops and certain government ministers, and other things don't, such as the assets these organisations may.
Also inherent in the definition is the notion that a legal form concerns how an organisation and its members are treated by the law in a particular jurisdiction. Different jurisdictions, with different laws, will allow a different set of legal forms for organisations.
Thirdly, "relate" refers to how the members co-operate to run the organisation, and to whether the organisation is treated a existing in its own right for legal purposes such as owning property and enforcing contracts.
This definition makes the word "category" do quite a lot of work: by category, the sense intended is that of a classification into sets which are mutually exclusive and collectively exhaustive. That is, an organisation has one and only one legal form: by this definition of category, and organisation can't have two legal forms at the same time, nor can it lack a legal form entirely.
Any organisations that exist de facto, if it ever ends up being considered by litigation or regulation, will be treated by the law as being only one kind of thing, such as a company or a partnership.
The legal system is also unlikely to be so ambiguous as to treat the same organisation as being of two different legal forms at the same time. To a great extent this is achieved by the fact that most legal forms involve registration, and the laws and procedures involved in registration operate such that it's not possible for the same organisation to be registered as two different types of thing. Additionally, there are often logical incompatibilities between the various legal forms, such as requirements relating to the objects of the organisation, or to whether the organisation has or lacks share capital.
Just because we're able to divide up the space of legal forms into exhaustive, mutually exclusive, categories does not necessarily mean that there can be a definitive list of what these categories are. This is because some of the categories could be further divided up into more categories. Let's say English law allowed only companies, registered societies and partnerships, and no other legal forms for organisations. Every partnership is either a limited partnership, or an LLP or a general partnership, and can't be more than one of these at the same time. So you could say that partnerships constitute three distinct legal forms, or you could say they all count as one, as they have so much in common, but are very different from companies and societies. This means there might be three different legal forms available, or five, depending on this choice.
This is known as the "lumpers and splitters" issue, and exists in other areas of taxonomy. For example, do Dutch and Flemish count as one language or two? There may often be no principled way to make the determination, and it may come down to taste.
Lumpers and splitters (Wikipedia)
There are statuses that all or some of the organisations sharing a legal form may have, which do not themselves constitute a separate legal form. For example, charitable status, or limited liability. It is important not to confuse these with the legal forms themselves, as they are classifications, not categories. Knowing that an organisation is a charity doesn't tell you how its members may remove a rogue member of the charity's governing body, or whether it is liable for all its debts: these depend first and foremost on its legal form, not additional statuses it may have.