Sole Proprietor : the person who owns and controls a sole proprietorship.
I am the sole proprietor of this business.
Or...
Independent Contractor : A person working independently, under a contract; a self-employed person.
I am an independent contractor.
Or...
Self-Employed (or Freelancer)
: working for yourself.
I am self-employed.
I am a freelancer.
english.stackexchange.com/users/1267/morganpdx
In Australia, they can be self-employed, freelancers, contractors, sole practitioners (for professional services), sole traders (for other services), and probably a lot more besides...
I don't know if I have heard of sole proprietors here.
english.stackexchange.com/users/3718/HorusKol
Sole proprietorship or simply proprietorship .
The owner is called the proprietor .
english.stackexchange.com/users/33533/Utsav
In the UK, a one person business is often referred to as a one-man band.
"My consulting business is actually just me.
I'm a bit of a one-man band at the moment"
It comes from the practice of a street entertainer playing multiple instruments at once.
english.stackexchange.com/users/47205/superluminary
The question is vague.
In the U.S, "sole proprietor" is a legal term that signifies the one human being who is responsible for the debts of a business and legally entitled to the profits of the business.
A sole proprietorship is distinguished legally from partnerships and corporations, in which the debts of a business are not the responsibility of a single, "natural person," another term of legal art.
In usual practice, a sole proprietor is also the daily manager of the business, but this need not be true.
Nor is it necessarily true that a sole proprietorship has only one person working at the business.
It refers to a technical legal relationship.
(See Wikipedia for "sole proprietor.")
In the U.S., one term commonly used for people who work for themselves is "self-employed," regardless of the legal form of ownership, which would not normally be known or of significance to most people.
That term, however, does not imply that the person works alone.
A person who owns and runs a small shop with several employees would still be called "self-employed."
A person who works alone may be called a "sole practitioner" or a "lone practitioner" although that term encompasses people who do not work alone so long as those with whom they work are in an auxiliary capacity.
Thus a doctor who is not in a group practice would be referred to as a sole practitioner even though the doctor may employ a nurse or secretary or receptionist, none of whom practice medicine.
EDIT
: I see the the OP was particularly interested in the incidence of taxation.
The entity that has primary liability for taxes depends on the exact legal form under which the business operates.
There is, however, a doctrine in U.S law called "piercing the corporate veil" that may impose secondary liability for corporate debts on other parties.
Moreover, U.S. tax law is arcane and Byzantine and so is the domain of highly specialized accountants and lawyers.
Any questions about primary and secondary liability for taxes should be asked of those specialists.
I won't even venture a guess.
english.stackexchange.com/users/241763/Jeff Morrow
The term self-employed without employees seems to be used by multiple organisations: Organisation for Economic Co-operation and Development (OECD) Eurostat (provides statistics for EU institutions)
The Dutch statistics agency Department for Business Innovation & Skills in the UK (powerpoint)
english.stackexchange.com/users/71848/JJ for Transparency and Monica
I'd rather think that proprietor means owner what, in turn, means that such person is not necessarily working in his/her business alone..
One person business would be the best..
english.stackexchange.com/users/298121/Jola
I'm wondering what is the term for the person, that is doing business on his/her own and has tax liability. It's different in each country, I'd like to know how they are called in USA and UK.
What is a one-person business called?
english.stackexchange.com
<terminology><business-language>
english.stackexchange.com/questions/10841
english.stackexchange.com/users/1426/lisak
A one-person business can be called many different names in both the USA and UK. A sole proprietor, for example, is someone who owns and controls a sole proprietorship. Other terms include "Independent Contractor", "Self-employed" or "Freelancer". In the UK, a one-person business is often referred to as a one-man band. In medical circles, a doctor who does not belong to a group practice may be described as a "sole practitioner". There are a number of suggestions such as "sole proprietor",  "self-employed", "freelancer" . A sole proprietor is usually the person who manages the business as distinct from legal partnerships or corporations. Some think "proprietor" means the owner, but does not necessarily work in their business alone. Another term is "Independent Contractor". None imply the person works alone. In the UK, the more informal term is "one-man band". Another US term is a "sole/lone" practitioner but may apply to specific professions such as doctors. In relation to tax liability, this can depend on the legal form of the business. Asking the expert here would be best.
A one-person business can be called many different names in both the USA and UK. A sole proprietor, for example, is someone who owns and controls a sole proprietorship. Other terms include "Independent Contractor", "Self-employed" or "Freelancer". In the UK, a one-person business is often referred to as a one-man band. In medical circles, a doctor who does not belong to a group practice may be described as a "sole practitioner". In the US, a (sole) proprietership is a legal term to designate a business where a natural person is responsible for the debts and entitled to the profits. 'Self-employed' is a common general term, but independent contractor, freelancer, sole trader and other terms can be used.
A one person business is called being self-employed and appears to be used by multiple organisations. Other terms include; sole proprietor or practitioner, independent contractor or freelancer. In the UK, a one person business is often referred to as a one-man band.    It is not clear whether there is much difference between usage in the UK and the USA, but some terms to describe a single-person business include "sole proprietor", "independent contractor" or "self-employed". In the UK, such a person is also often referred to as a "one-man band".
One-man band Sole/lone practictioner The party who has tax liability will be determined by the business' legal form. Ask the specialist.
In the US, a (sole) proprietership is a legal term to designate a business where a natural person is responsible for the debts and entitled to the profits. Self-employed' is a common general term, but independent contractor, freelancer, sole trader and other terms can be used.
There are range of terms to describe such a person, including "Sole proprietor", "independent contractor" or "self-employed". In the UK, a one-person business is often referred to as a "one-man band".