Embedded system is the term used to any computing system that is used to perform a limited or specialized task. Unlike a general purpose computer that can perform a wide variety of tasks and is very complex, an embedded system is rather simplistic and does not have unnecessary hardware. ATMs, routers, calculators, and mobile phones are a few examples of devices that have embedded systems in them.
On the other hand, VLSI stand for Very Large Scale Integration, which is a term used to describe the complexity of an integrated circuit by giving a generalized idea of how many transistors are within the circuit. Integrated circuits that contain thousands of transistors in a single package are classified as VLSI with other terms like MSI or ULSI among others, used to describe other integrated circuits with fewer or more transistors.
We can say that VLSI is a part of an embedded system.
Also now VLSi has been taken over by the ULSI(ultra large scale integration)