What is the difference between stochastic process and random variable? I am having a hard time grasping the core difference between a random variable and a stochastic process.

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*A random variable assigns a number to every outcome of an experiment.

*A random process assigns a function of time to every outcome of an experiment.
But the values of this function of time can be represented with ONE SINGLE random variable as well. So what is the point in having a stochastic process when you can represent an experiment with only random variables? Could somebody make one or two examples where the difference is clear?

Appreciate it

You say, "A random process assigns a function of time to every outcome of an experiment."  No.  A random process could be a function of time.  At every time, the value is a random variable.  I'll give two examples, one where the process domain is discrete, and one where it's continuous.
First, consider a gambler who repeatedly plays a game, which he wins with probability $p<\frac12$.  If he wins, he gains one dollar, otherwise he loses one dollar.  He continues until he runs out of money.  Let $X_n$ be the gambler's bankroll after $n$ plays, where his initial bankroll is $X_0=B$ for some positive integer $B$.  We can say that once the gambler runs out of money, his bankroll is always $0$, so that $X_n$ is defined for every $n\geq 0$.  Each $X_n$ is a random variable.  For example, $X_1$ is $B+1$ with probability $p$ and $B-1$ with probability $1-p$.  The whole sequence $$X=X_0,X_1,X_2,\dots$$  is a stochastic process.  (Obviously, $X$ depends on $B$ and I should really write $X(B)$ or something like that, but I suppress that.)
Here's an example of a continuous domain.  Let $Y(t)$ be the temperature in a specific location on a summer day, where $t=0$ is midnight, and $t=24$ is midnight the following day.  Then $Y(t)$ is a random variable, for every $)\leq t\leq24$.
I'm not sure I understand what's giving you difficulty, but you may be confusing a random variable and its value.  It's true that if we take frequent readings of the temperature, we can make a graph showing what the temperature was throughout the day, but those are the values, not the random variables themselves.  For example, we may find that the temperature at noon was $85^\circ$F, but that doesn't mean $Y(12)$ is the number $85$.  $Y(12)$ is a random variable, distributed according to the probability distribution at that location in the summer.  $Y(12)$ tells us things like, "The temperature at noon will be between $80$ and $90$ degrees with probability $.65$."
