Lifetime estimation - Weibull vs Survival Survival analysis is mainly about estimating the lifetime of nearly anything or even anything:

And Weibull analysis is also about estimating the lifetime:

How are they different (in general) and which should be used when?

If the failure times have a distribution $F(t)$ then the corresponding survival function is $S(t)=1-F(t)$. That's a critical thing to keep in mind.
The Weibull plots are just plots of a transformed $F(t)=1-S(t)$ against the log of time. So the Weibull plot is just a particular replotting of the survival curve.
A Weibull model can be written in the form:
$$\log T= \alpha + \sigma W, $$
where $W$ has a minimum extreme-value distribution and $\sigma$ is a scale factor. The y-axis transformation of $F(t)$ in a Weibull plot gives a straight line if the underlying distribution $W$ is minimum extreme-value. If there is a well fitting line, then the values of $\alpha$ and $\sigma$ can be deduced from the plot.
My sense is that the plots were most important before modern computational technology became available. I don't see that there's anything they do that can't be done with more general survival modeling, which doesn't restrict you to a Weibull form. You can always generate a Weibull plot from your survival model if you want to.
