MEMS is combination of electronic and mechanical system in a single chip,while nanotechnology consist of eveyrthing which of nanometre lenght,even chemical,physical and biological systems,anyhow MEMS are bigger than nano-systems.
Thats about it. A MEMS chip consists of different parts; the microelectronics,the microsensors, microactuators, microstructures, and are fabricated together using microfabrication techniques (like IC's). The benefits of MEMS are limitless!
I believe the basic difference between MEMS and Nanotechnology is the size: MEMS are typically between a micrometer (10-6m) and a millimeter (10-3m), while nanotech is in the nanometer scale (10-9m). Because we go down to such a small scale, we make use of the properties of the materials down at the nanoscale.
It's quite amazing though... We can achieve remarkable sensitivities and precision using the MEMs technology when it comes to electromechanical sensor and actuators. For eg., consider the accelerometer...its made up of a spring, a mass and a damper... the natural frequency is given by sqrt(k/m).. that means, when the mass is taken to the 'micro' level, you have an extremely sensitive accelerometer with great resolution.. Its amazing, MEMs...
As far as Nanotech is concerned, when you're down to the nano scale, everything is in its 'primordial' form. It's all broken down to the level of bio-chemo-physical molecules. There are a few researchers at my university who have done breakthrough research in this field. We recently bought a Nano-Indentation machine as well. Also, its usually the materials engineers with a know-how in biochemistry who usually pursue this research. Also, your maths has to be great.
MEMS is the integration of a number of microcomponents on a single chip which allows the microsystem to both sense and control the environment. The components typically include microelectronic integrated circuits (the “brains”), sensors (the “senses” and “nervous system”), and actuators (the “hands” and “arms”). The components are typically integrated on a single chip using microfabrication technologies similar to those used for integrated circuits.
Nanotechnology takes advantage of the observation that at the nanoscale, properties of materials change. Nanotechnology is that array of technologies that use properties of materials that are unique to structures at the nanoscale.