Difference in usage of terms "company" and "firm"

In a meaning of officially registered and bounded business unit. Like "Microsoft" or "Apple" or "ZARA" or copy shop round the corner.
In some books on management/entrepreneurship authors use both words interchangeably without understandable logic. Somewhere I heard that "company" is mostly about a smaller business than "firm".
I tried to ask people around me (they are actually not native English-speakers, but more close to them than me - Netherlands) but their proposals sometimes were almost opposing.

In some cases ex. "law firm" it's more like a set phrase, but what could be a general approach?

Companies

I will explain to you the position in the United Kingdom which was where the notion of the joint-stock, limited liability company originated, which idea has been adopted in different forms around the world.

The word 'Company' has a legal significance. In the case of a properly registered company the liabilities of the members (shareholders) are limited to the amounts they have agreed to subscribe.

Businesses registered with the Registrar of Companies in this way are called 'Companies'. There are two types. There is the 'Public Limited Company', which has the appendage PLC after its name. These are the largest organisations and the PLC aspect means that their shares are traded on a stock exchange, usually the London exchange. In many cases their total assets run to many billions of pounds. Examples would be BP PLC, or British Aerospace PLC. However some quite small companies are registered as PLC's and their shares are traded. When a small company takes on a stock-market listing it is known as 'flotation'.

The other kind of limited liability comany is the 'private company'. The members' liabilities are limited in the same way as with PLCs, but their shares are not traded. And any transference of share ownership has to be approved by a majority vote of shareholders. These companies have the appendage Ltd., after their names e.g. Norwich City Football Club Ltd, The Delightful Foods Restaurants Company Ltd. etc.

Often large Companies own smaller companies and many are formed into groups of companies. But still the overall group is usually referred to as a 'Company', sometimes as a 'Group'.

Firms

Sometimes the Companies I have described above are referred to, informally, as 'firms', even the very largest ones. The fact that this happens in no way changes the fact that they are legally Registered Companies.

Businesses which are not registered as Compnies come in two forms. Either they are sole proprietorships owned by one person, or they are partnerships. In either case the owners liabilities are not limited. Partners and Proprietors are personally liable, jointly and severally for the debts of the business.

These businesses are nearly always called 'firms'.

Some professional practices e.g. solicitors, accountants etc are not allowed to adopt limited liability under the rules of their professional bodies, e.g. the Law Society or the Institute of Chartered Accountants. These professional practices are nearly always called 'firms'. They also include such as consulting engineers, insurance brokerages, etc. Their names do not have to include the appendage Ltd or PLC.

So, in summary, a 'firm' can mean any type of business, but usually the appellation implies that it is not registered as a company. A 'company' is a business which is registered with the Registrar of Companies and is subject to the Companies Acts.

Corporations

The term Corporation does not have legal significance in the UK, though some Companies are called Corporations, albeit with the appendage PLC or Ltd after its name. Corporation is a term that is far more widely used in the United States. Indeed their equivalent of PLC or Ltd is 'Inc', short for 'incorporated'.

This question must be examined from two main perspectives:

• Legal perspective and;
• Linguistic perspective.

From legal perspective there is no such business structure as firm. The word "firm" is used interchangeably with the term "company".

From a linguistic point of view company is a broader notion of business entity. The notion of “company” embraces the notion of “firm”. In simple words, all business entities are usually referred as companies. Only those of companies that are partnerships are usually referred as firms. (E.g. law firms, accounting firms - those are usually partnerships)

Source

Traditionally, firm has been used for a business that operates as a partnership -- hence law firm, accounting firm, etc. -- and this practice continues with professional trades, even when they are plied using a professional corporation rather than a partnership (Hence, you wouldn't say law company or accounting company). For all other types of businesses, the terms are pretty much interchangeable, regardless of the business entity.

It is common, however, to use firm for larger entities. You might call a business run from someone's garage a company, but it would sound odd to refer to it as a firm.