What is the difference between heat and light?
In physics, heat is energy that spontaneously passes between a system and its surroundings in some way other than through work or the transfer of matter. When a suitable physical pathway exists, heat flows spontaneously from a hotter to a colder body.The transfer can be by contact between the source and the destination body, as in conduction; or by radiation between remote bodies; or by conduction and radiation through a thick solid wall; or by way of an intermediate fluid body, as in convective circulation; or by a combination of these.
(Source: Wikipedia)
So, to put it simply, we talk of "heat" whenever there is transfer of energy without work or transfer of matter. This is what is stated in the first law of thermodynamics:
$d U = \delta Q - \delta W$
which holds for a closed system (we rule out the transfer of matter).
The variation of the internal energy of a closed system which is not due to work is what we call "heat".
The word "light" usually refers to visible light, that portion of the electromagnetic spectrum whose wavelength is between $\sim400$ and $\sim700$ nm. But we can more generally talk about "electromagnetic radiation" and consider the whole spectrum.
As stated in the Wikipedia article I quoted, heat can be radiation between two bodies. This just means that the "$\delta Q$" in the first law of thermodynamics can be due to electromagnetic radiation.
Every body at a temperature $T$ different from $0$ will emit electromagnetic radiation (thermal radiation). This is because the atoms inside the material are moving, and this causes accelerations and decelerations of the charged particles the atoms are made of, and therefore electromagnetic radiation.
Therefore, an object at temperature $T$ will emit electromagnetic radiation in the surroundings (which are at temperature $T_e$) and absorb radiation from them. At the same time, the surroundings will emit and absorb electromagnetic radiation in the same way. The higher the temperature, the more the radiation.
This process will stop only when $T_e=T$, because then the absorbed radiation will be equal to the emitted radiation. So, the object and its surroundings will start at different temperature and end up having the same temperature. Since temperature and internal energy are related, this will mean that the internal energy of the bodies has changed. Seeing as how there has been no work or transfer of matter, we call heat this change of energy, which was due to electromagnetic radiation.
This one of the possible connections between heat and electromagnetic radiation.
Update: clarification
Of course there is also EM radiation which isn't thermal, i.e. it is not originated by the acceleration/deceleration of charges due to random motion. An example is given by transition between atomic energy levels, which is the mechanism behind the laser. This kind of radiation can of course be used to transfer energy without work/transfer of matter, so it is a kind of heat. The EM radiation is always the same: what changes is the mechanism originating it.
It is also clear that you can have heat without EM radiation. For example you put two objects in contact and transfer energy by conduction.
To sum up: heat is a change in energy without work/transfer of matter. This transfer can be realized via EM radiation or via other means (conduction, convection etc.). Also, EM radiation can originate in different ways: thermal motion, electronic transitions etc.
Also they are closely related in empirical life, they are different and the concepts come, I would claim, from different theories.
Light is electromagnetic radiation in the visible spectrum which is produced by moving charges according to Maxwell's equations.
Heat is a thermodynamical concept and usually describes energy transfer that is not work (or energy transmitted through particle transport). Heat is not something inherent to a body but only a quantity transfered from one to the other. The light waves, when they fall onto an object, cause the body to heat up, i.e., to have a higher temperature. This has nothing per se to do with heat. Temperature can be understood as the speed of molecular motion - and as moving charges emit radiation, moving molecules do so too. This is why objects emit radiation. The spectrum of that emission is, in easy cases, given by the Stefan-Boltzmann-Law/Planck's law and from it you can see that warm bodies emit more electromagnetic radiation.
I hope my explanation does not have any major flaws and I could shed a bit of light on the matter.
A simple answer is that light has energy, whereas heat is a form of energy.
It is similar to the difference between a billiard ball and the kinetic energy of the billiard ball
Electromagnetic radiation classically is described by fields, but in the underlying quantum mechanical framework it is emergent from a confluence of an enormous number of photons. Photons, elementary particles , similar to the billiard balls, have energy but are not energy.
You state:
What i know is that light is an electromagnetic wave.
True, and more so , it is an emergent phenomenon from a multitude of photons.
Is heat also an electromagnetic wave of certain wavelength other than light ?
No. Heat is a macroscopic thermodynamic energy variable which , together with energy conservation, describes thermodynamic systems.
Energy:
In physics, energy is a property of objects which can be transferred to other objects or converted into different forms. The "ability of a system to perform work" is a common description, but it is misleading because energy is not necessarily available to do work. For instance, in SI units, energy is measured in joules, and one joule is defined "mechanically", being the energy transferred to an object by the mechanical work of moving it a distance of 1 metre against a force of 1 newton. However, there are many other definitions of energy, depending on the context, such as thermal energy, radiant energy, electromagnetic, nuclear, etc., where definitions are derived that are the most convenient.
So objects have energy, and light waves have energy, they are not energy.
You ask:
Why the light wave cause heat in an object when it falls on the object ?
Photons, light, hitting and being absorbed by an object leave their energy in the atoms of the object, kinetic or vibrational. The kinetic and vibrational energies of the atoms in a medium define the heat energy of the medium. The photons are absorbed by the quantum mechanical levels of the medium.
and why does an electric heater emits light ? It means both of these are very closely related but i am not understanding the relation between the two?
Yes, they are related. The quantum mechanical levels of the atoms in a medium which can absorb photons ( electromagnetic waves) also emit them if in an excited state. The energy for emission in a heater, i.e raising the atomic levels so that they can relax and emit a photon, is given by the electricity supply.