Hello Ashwin,
That is a very good question. Projectized and Strong Matrix organizations appear to be very similar in essence. The primary difference between these organizational structures is the Project Manager's authority and influence on the project.
For instance, a PM will lead a project through a Strong Matrix organization but they normally do not carry the authority to make financial decisions that could significantly impact the project. In this type of scenario the PM will need to gather approval from a functional stakeholder, such as the CFO or a Finance Director prior to making financial decisions relating to the project. In a Projectized organization the PM will most likely have the full capacity and authority to make these types of decisions.
The managerial aspects of a project are executed by a functional manager in a Weak Matrix organization and possibly a Project Expeditor/Coordinator or functional manager in Balanced Matrix organizations. Designated functional managers will always take control of the project in Functional Organizations, however it is possible that they are openly referred to as the PM during the project's lifecycle.
Did I do a good job explaining this? Please refer to the PMBOK 5th Edition under Table 2-1 to better follow along with the concepts.