Equation of straight line I know,
$Ax + By = C$
is the equation of straight line but a different resource says that: 
$y = mx + b$ 
is also an equation of straight line? Are they both same?

Yes. That is, they both give the equation of a straight line and the equation of any non-vertical line can be written in either form.
If $B\ne 0$. Then you can write $Ax+By=C$ as
$$
By=-Ax+C 
$$
and, since  $B\ne0$, the above can be written
$$
y=-\textstyle{A\over B}x +{C\over B}.
$$
If $B=0$, the equation is $Ax=C$, which is a vertical line when $A\ne0$. In this case you can't write it in the form $y=mx+b$ (which defines a function).
On the other hand, given $y=mx+b$, you can rewrite it as $-mx+y=b$.



Note that for the equation $Ax+By=C$ with $A$ and $B$ both non-zero:

The $y$-intercept of its graph is $C/B$ and is found by taking $x=0$.
The $x$-intercept is of its graph is  $C/A$ and is found by taking $y=0$. 
The slope of the line is then $ {C/B-0\over 0-C/A } = -A/B$.

