Are calculus and real analysis the same thing? 
*

*I guess this may seem stupid, but
how calculus and real analysis are
different from and related to each
other?
I tend to think they are the same
because all I know is that the
objects of both are real-valued
functions defined on $\mathbb{R}^n$,
and their topics are continuity,
differentiation and integration of
such functions. Isn't it?

*But there is also
$\lambda$-calculus, about which I
honestly don't quite know. Does it
belong to calculus? If not, why is
it called *-calculus?

*I have heard at the undergraduate course level, some people mentioned the
topics in linear algebra as
calculus. Is that correct?


Thanks and regards!

My take on this: One would use the word 'calculus' when one is applying the mathematical tools - chain rule, integration- by-parts, etc - to solve problems in science, engineering, and so on; whereas one would use the word 'analysis' when one is developing/justifying the same tools - proving the chain rule, inventing integration-by-parts, etc.  I.e, analysis is what the pure mathematicians do, calculus is the product of analysis which engineers use.
