What is difference between sound waves and light waves?

Yes, both are waves but there characteristics are different. And these characteristics also make the difference in how we perceive them.

So to answer this question we need to understand two things - 1) wavelength and frequency of the waves and 2) diffraction.

Wavelength from wikipedia -

In physics, the wavelength of a sinusoidal wave is the spatial period of the wave—the distance over which the wave's shape repeats. It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a characteristic of both traveling waves and standing waves, as well as other spatial wave patterns. Wavelength is commonly designated by the Greek letter lambda (λ).

Check out this figure below -

Frequency, as you would have guessed, is inverse of the wavelength.

The wavelength of light is in the range of nanometers. For example in visible colors, red light has the longest wavelength, while violet has the shortest. Visible light wavelengths are between 400 and 700 nanometers. Wavelengths smaller than 400 nanometers get into ultraviolet, X-ray, and gamma-ray territory; wavelengths greater than 700 nanometers comprise infrared, microwaves, and radio waves.

The wavelength of sound is in the range of meters or centimeters. For example, a low-pitched sound would have a wavelength of about 15 meters and high-pitched sounds would have wavelengths of around 2 centimeters.

So how does wavelength answer the question that we can hear across the wall but cannot see. To answer this, lets understand what is diffraction. Diffraction refers to various phenomena which occur when a wave encounters an obstacle. Diffraction can happen with all types of waves. There is very thin line between diffraction and interference and sometimes they are used interchangeably.

The effects of diffraction are more pronounced when the wavelength of the wave is roughly similar to the size of the diffracting objects. So now, you might have guesses the answer. The wavelength of light is very small while the openings across the rooms (through doors, windows etc) is very large. But the wavelength of sound is comparable and thats why diffraction occurs in sound waves across the wall and not in light. Can you give examples where diffraction happens with light waves and not sound waves?

Check out this wiki page to know more about diffraction - http://en.wikipedia.org/wiki/Diffraction