Difference between "Random motion" and "Brownian motion"? I know "Random motion" is non-deterministic unpredictable motion of a particle. But it seems "Brownian motion" has some form of determinism as we can predict the pattern created by path taken by particle in long term. 
What's the main difference between these two kinds of motion?
 A: Brownian motion has a very specific meaning: the motion of small particles suspended in a fluid. The motion is due to the random collisions between the molecules of fluid with the particles in suspension. So Brownian motion does not refer to the thermal motion of the molecules but is an effect of this molecular motion on particles much larger than one molecules. However the particles have to be small enough so that the effects of collisions with many molecules do not average to zero (or to values to small to matter). 
Both molecular motion and Brownian motion can be called "random" (or not) depending of the meaning we associate with this concept of "randomness". 
Ideally, if ones knows the positions and velocities of all molecules at a given time, we could in principle predict next configuration for both molecules and particles in suspension.
But if you consider thermal motion as an example of random motion, then Brownian motion is a more specific example of the general term "random motion".
A: Random motion is a generic term which can be used to signify that a particular system's motion or behaviour is not deterministic, that is, there is an element of chance in going from one state to another, as oppose to say, for example, the classical harmonic oscillator.
On the other hand, Brownian motion can be thought of as a more specific condition on the random motion exhibited by the system, namely that it is described by a Wiener stochastic process, which is made rigorous by probability theory and stochastic calculus. 
One of the key features is that given a random time-dependent variable $X(t)$, and a set of times $t_1, t_2$ and so forth at which we measure $x_1, x_2 \dots, x_n$, there are a set of joint probability distributions,
$$p(x_1, t_1 ; x_2, t_2; \dots)$$
which describe the system. In physics, we (mostly) deal with separable processes, entailing,
$$p(x_1, t_1 ; x_2, t_2; \dots) = \prod_n p(x_n,t_n)$$
which is to say that $X(t)$ is entirely independent of whatever happens in the past or future. (For a Markov process, one has only the present determines the future.) To relate this to something you may be more familiar with, if $p$ were independent of $t$, you could have Bernoulli trials, like coin flipping, where the same probabilistic laws describe the behaviour at all times.

The key point is $X(t)$ cannot be known definitively at any time $t$, but by deciding what type of process it is, or by making certain assumptions, we can make probabilistic statements about it, of observables. For example, the Langevin equation for a mass in a medium subjected to noise is,
$$m\ddot{\vec{x}} = -\gamma \dot{\vec{x}} - \nabla V + \vec{f}(t)$$
where $\vec{f}(t)$ is the random noise, and $V$ is a potential. In the case of $m = 0$ and $V=0$ for simplicity, although we cannot write down deterministically $\vec{x}(t)$, it can be shown (under assumptions),
$$\langle \left( \vec{x}(t)-\vec{x}(0)\right)^2 \rangle = \frac{1}{\gamma^2} \int_0^t dt'_1 \int_0^t dt'_2 \, \langle \vec{f}(t'_1) \cdot \vec{f}(t'_2) \rangle$$
that is, we can comment on the variance of position based on correlation functions of the noise. If we assume a delta distribution for $\langle f_1 \cdot f_2 \rangle$, the noise is white noise, and $\vec{x}(t)$ is what we call Brownian motion, with a root-mean-square distance going as $\sqrt{t}$.  
This does not mean $\vec{x}(t)$ is not random, it simply means we can comment on the way statistical properties of the system evolve with time.

Additional Resources
Handbook of Stochastic Methods provides a readable introduction to stochastic calculus, with applications to physical problems.
If you'd like to see how this can be applied to something less 'mainstream', The Theory of Polymer Dynamics by Doi and Edwards is an excellent and thorough text in which some of these methods, among others, are used to study the dynamics of polymers. (No chemistry or biology knowledge needed at all.)
A: 
I know "Random motion" is non-deterministic unpredictable motion of a particle.

Random motion refers to the movement of any object, and uses the definition of the word random as it used in ordinary language, that is unpredictable and seemingly nondeterministic. Although I should stress that truly random motion, or random anything in nature,  is almost always pseudorandom, in that there is generally a pattern to it in some sense, it is simply hidden under varying levels of  complexity.
I can think of only one phenomenon that can produce the most accurate version of true randomness. Take a lump of any radioactive material, with a suitable short half life. Arrange a mechanism to provide motion in any direction to say, a toy car. Then every time there is a radioactive decay, it would set the toy car off in an unpredictable pattern.

But it seems "Brownian motion" has some form of determinism as we can predict the pattern created by path taken by particle in long term.

Brownian motion is specifically the apparent motion of atoms and molecules, on a microscopic scale in a fluid medium. Again it could/should  be classed as pseudorandom, as there are often obvious cause and effects involved. For instance,  if water molecules are heated they will increase their motion in accordance with various well known physical laws, such as the Maxwell probability law relating to velocities. 
So Brownian motion may in general be considered less random than other forms of randomness, it would need a comparison on a case by case basis to establish which motion is more influenced by randomness. 
