Idaho "corporation", "incorporated", "company", "limited", or the abbreviation "corp.", "inc.", "co.", or "ltd.", or words or abbreviations of like import in another language; provided however, that if the word "company" or its abbreviation is used it shall not be immediately preceded by the word "and" or by an abbreviation of or symbol representing the word "and" § 30-1-401 Idaho Statutes
Limited liability companies can raise money via banks and investors but cannot sell stocks. S-Corps can get loans from banks, as well as distribute stock to up to 100 people. C-Corps have the easiest time raising capital as there is no cap on how many people can own stock. Non-Profits can both get loans and receive tax-deductible donations. Sole Proprietorships can occasionally receive bank loans but cannot sell stocks.
Corp., Inc., Corporation, Incorporated: used to denote corporations (public or otherwise). These are the only terms universally accepted by all 51 corporation chartering jurisdictions in the United States. However, in some states other suffixes may be used to identify a corporation, such as Ltd., Co./Company, or the Italian term S.p.A. (in Connecticut; see under Italy). Some states that allow the use of "Company" prohibit the use of "and Company", "and Co.", "& Company" or "& Co.". In most states sole proprietorships and partnerships may register a fictitious "doing business as" name with the word "Company" in it. For a full list of allowed designations by state, see the table below.
On the other hand, if you are not responsible for its tax, then you should declare the equipment in Part III of the Business Property Statement (Equipment belonging to others). Where equipment is declared in Part III of the Business Property Statement, the Assessor will also send a Notice to File to the person reported as the equipment's actual owner.