Inc. is the abbreviation of English incorporated, which is often used in American English. In Britain, the abbreviation of limited company is Co'Ltd
A company limited by shares represents the nature of a company.
Company Limitid is usually abbreviated as Co.ltd or ltd for short, but this only means that the company is a limited company, not any other company. There should be no company between the company name and Co.ltd, because co. already contains the meaning of company.
Besides, the prototype of Inc. is Incorporation, which means: company formation/registration/merger. If it is added after the company name, it is mostly in the form of participle, but it has become an inherent descriptive vocabulary: Incorporated. If you use this usage, it is mostly American, and you don't even add Ltd. But its meaning is:' a company limited by shares' focuses on the limited company with the nature of' shareholding system', that is,' formed by branches' and' formed into a (joint-stock) company'.
In British usage, Limited can be added directly after the company name. It means the same thing as Inc.