Series OF ISO 9001 Standards

ISO 9001 includes the following standards:
•ISO 9001:2008 Quality management systems Requirements is intended for use in any organization regardless of size, type or product (including service). It provides a number of requirements which an organization needs to fulfill to achieve customer satisfaction through consistent products and services which meet customer expectations. It includes a requirement for continual (i.e. planned) improvement of the Quality Management System, for which ISO 9004:2000 provides many hints.
This is the only implementation for which third-party auditors can grant certification. It should be noted that certification is not described as any of the 'needs' of an organization as a driver for using ISO 9001 (see ISO 9001:2000 section 1 'Scope') but does recognize that it may be used for such a purpose (see ISO 9001:2000 section 0.1 'Introduction').
•ISO 9004:2000 Quality management systems - Guidelines for performance improvements covers continual improvement. This gives you advice on what you could do to enhance a mature system. This document very specifically states that it is not intended as a guide to implementation.
There are many more standards in the ISO 9001, many of them not even carrying "ISO 900x" numbers. For example, some standards in the 10,000 range are considered part of the 9000 group: ISO 10007:1995 discusses Configuration management, which for most organizations is just one element of a complete management system. ISO notes: "The emphasis on certification tends to overshadow the fact that there is an entire family of ISO 9000 standards ... Organizations stand to obtain the greatest value when the standards in the new core series are used in an integrated manner, both with each other and with the other standards making up the ISO 9000 family as a whole".
Note that the previous members of the ISO 9000 series 9002 and 9003 have been integrated into 9001. In most cases, an organization claiming to be "ISO 9000 registered" is referring to ISO 9001.