What is an electron? Is it an orbital? Is an orbital a wave or is an electron a wave? Does an electron exists in an orbital or is an orbital a wave cloud of electrons? Is there really particle inside an orbital or is an orbital a particle?
 A: Physicists do not all agree on the answer.
The orbital is sometimes likened to a "cloud" across which the wave function is distributed. Mathematically the wave function gives the probability of the electron being detected at any given point in the cloud at any given moment of measurement.
Some physicists have suggested that the electron basically is the wave, and the probability distribution in measurement arises as a result of that. Some have suggested that the electron is a particle and the wave somehow "pilots" it to its position at the time of measurement according to some hidden variables we are unaware of. According to quantum field theory it is a disturbance in the zero-point electron field (whatever that means!). And so on.
Ultimately, all a physicist can say is that an electron is the subject of some particular mathematical equation that is good at predicting experimental results. The commonest view is therefore to stop thinking about it because it is impossible to know the underlying answer, best to just "shut up and calculate."
A: Hi and welcome to stackexchange. 

Is orbital a wave or electron is a wave.

The electron is associated with the wave $\psi(\vec{r})$ in quantum mechanics. The orbital, as it is pictured in textbooks, is similar but not the same: it is $|\psi(\vec{r})|^2$. That is because $\psi(\vec{r})$ is a complex number, so it cannot be plotted as a shape in a volume. You also have to be a bit careful: the wave is not a wave in space, it is a wave which is defined in configuration space, which is the space of all possible configurations of the particles. So, for 2 or more particles, you have $\psi(\vec{r}_1, \vec{r}_2)$, and there is no straightforward way to associate the wave to a volume in space.

Did electron exists in a orbital or orbital a wave cloud of electron. Is there really particle inside orbital or orbital is a particle

Humanity doesn't have a proof of that either way. It may be that the electron is a wave, or that some other description is possible. Most physicists go with the "electron is a wave" interpretation. However, for example, there is a near-equivalent theory called Bohmian Mechanics in which the electron is associated with both a wave and a particle.
A: 
What is an electron? 

It is an elementary particle, one of the particles in the standard model of particle physics, of charge -1 and lepton number 1. I has been studied in beams in cathode ray tubes since the 19th century, and in beams in the twentieth century, and its particle nature can be seen in this double slit experiment, one electron at a time.

The particle nature is seen in the footprint of seemingly random dots in the top frame, and the wave nature is seen clearly in the probability distribution given by the accumulation of electrons in the bottom frame, clearly showing interference effects characteristic of waves.

Is it an orbital?

No, all particles in a bound state have orbitals, not orbits. Orbitals are locus of probability, giving the probability of measuring the particle at a specific (x,y,z). The mathematical equivalent of the probability distribution in the scattering of electrons from the  double slits above.
For hydrogen, this is what one would observe doing an experiment of locating electrons in the various energy levels.

This experiment has been done, see here.


Their system used tunable lasers to excite electrons in a hydrogen atom placed in an electric field. An electrostatic lens then stretched and magnified the orbitals — without disturbing the internal structure — until individual electrons hit a detector. After recording about 50,000 electrons, the team produced images to show the structure of the electron orbital (pictured) of atoms at different excited states.

So, theelectron is a particle and depending on the boundary conditions being the same, the probability distribution of its location can described as the wavefunction of an orbital.
