Comparing interaction potential in standard $ϕ^4$theory

I am posting this question again because, Willie Wong asked me to do it. So it is a continuing post of the Interaction potential in standard ϕ4 theory.

I have been studying about solitions so I had to deal with scalar field theory. The problem I faced in Lagrangian of Scalar field is interacting potential.

According to Scalar field theory we can write: $$\mathcal{L}=\frac{1}{2}\partial^\mu \phi \partial_\mu \phi -\frac{m^2}{2}\phi^2 -\frac{\lambda}{4!}\phi^4 \tag {1}$$ The potential can be written separately $$V(\phi)= \frac{m^2}{2}\phi^2 +\frac{\lambda}{24}\phi^4 \tag {2}$$ I found on Srednicki (Quantum Field Theory, page 188) that, the author wrote the potential as, $$V(\phi)= \frac{1}{24} \lambda (\phi^2- v^2 )^2-\frac{\lambda}{24} v^4 \tag {3}$$ After that the author excluded the term $-\frac{\lambda}{24} v^4$.

why is that?

In another paper an author wrote the potential as $$V(\phi)= \frac{1}{8} \phi^2 (\phi -2)^2 \tag{4}$$
I don't see coupling constant $\lambda$ in the equation (4).

What I'm trying to find is to get the potential in equation (4) from the equation (2)