Question

What is the difference between $\log$ and $\ln$ ?

Answer 1

They are not the same. They are both logarithms, but they are different logarithms.
Explanation:
There's a huge difference between $\log$ and $\ln$
A logarithm is a form of math used to help solve the following sort of problems:
$a^x=b$
The question you're asking here is to what power do I need to raise $a$ to get $b$? This exact thing can be said using logarithms (as shown below):
${\log }_{a}b=x$
The relationship between logarithms and exponents is described below in given figure.
That value $a$ there is what we call our base, and it can vary based on what problem you're trying to solve.
When you have a base $10$, then it's convention to just drop the base from the notation, since it's implied that you're talking about a base of $10$.
So $\log \left(3\right)$ and ${\log }_{10}\left(3\right)$ are one and the same thing, the same way $x$ and $1x$ are the same thing: they tell you the same thing, but one has superfluous information.
When you have a base $e$, you switch to $\ln$, and again drop the base from your notation.
So $\ln \left(3\right)$ is the exact same thing as ${\log }_e\left(3\right)$.
As you can see, $\log \left(x\right)$ and $\ln \left(x\right)$ are not the same thing. They involve the same concept, and are both logarithms, but they are still different things.