LLC, LC, Ltd. Co., Limited Liability Company: a form of business whose owners enjoy limited liability, but which is not a corporation. Allowable abbreviations vary by state. Note that in some states Ltd. by itself is not a valid abbreviation for an LLC, because in some states (e.g. Texas), it may denote a corporation instead. See also Series LLC. For U.S. federal tax purposes, in general, an LLC with two or more members is treated as a partnership, and an LLC with one member is treated as a sole proprietorship.
New York Shall contain the word "corporation", "incorporated" or "limited", or an abbreviation of one of such words; there is also a long list of words a business corporation is not allowed to use without additional approval from other agencies including "board of trade", "state police", "urban development", "chamber of commerce", "state trooper", "urban relocation", "community renewal", "tenant relocation", "acceptance", "endowment", "loan", "annuity", "fidelity", "mortgage", "assurance", "finance", "savings" and many others New York State Consolidated Laws, Business Corporations Law § 301; Not-For-Profit Corporations Law, § 301
LP, Limited partnership: a partnership where at least one partner (the general partner, which may itself be an entity or an individual) has unlimited liability for the LP's debts and one or more partners (the limited partners) have limited liability (which means that they are not responsible for the LP's debts beyond the amount they agreed to invest). Limited partners generally do not participate in the management of the entity or its business.
In this case, you need to write a remark about that circumstance on the Business Property Statement, or on an attachment to it. Also fill out Part III (Equipment Belonging To Others) of the form. If you own any small equipment, such as a printer, copier, etc., that you are using in the business, you should report these costs under Part II of the Business Property Statement and also Schedule A.