My company is Ltd. It's a big multinational owned by public shares and on the stockmarket.
If it's quoted on a stock market, it will not be a private ltd company because it'll be in flagrant breach of the Companies Act 2006 if it is.
For the record, any UK company that is a PLC will ge one that complies with the various Companies Acts requirements for being a PLC. The full detail of that is quite fussy, but the gist of it is what weringo previously said, including
- registered as or to converted to PLC
- shares can be offered to public
- minimum £50000 share capital, of which minimum 25% must be paid up
The CA2006 is very specific, in Part 20, Ch1, s755 to be exact, that a private limited company CANNOT offer any security (shares or debentures) to the public, or allot or allocate them with a view to doing so.
There are all sorts of other differences, such as more onerous reporting requirements, a requirement for the company secretary to be a qualified professional, more than one director, and so on, but the two primary differences are the share capital requirements and the fact that private limited companies cannot have shares offered to the public.
That severely limits capital-raising options, because the company has to find buyers for shares privately, not just via public offerings, and there will usually be restrictions requiring all shareholder's approval before issuing new shares to pevent dilution of stakes, etc.
So, to summarise, a PLC is a company limited by shares or guarantee that complies with the CA2000 (etc) requirements, the primary two requirements being as above.
A private company is any company that is not public.
Oh, and the inclusion of PLC in the name is a very good guide, but not 100% reliable as there are some special exemptions to that.