  In a previous work [Phys. Rev. A 85, 022502 (2012)] we calculated, with the
use of our Gaussian expansion method for few-body systems, the energy levels
and spatial structure of the 4He trimer and tetramer ground and excited states
using the LM2M2 potential, which has a very strong short-range repulsion. In
this work, we calculate the same quantities using the presently most accurate
4He-4He potential [M. Przybytek et al., Phys. Rev. Lett. 104, 183003 (2010)]
that includes the adiabatic, relativistic, QED and residual retardation
corrections. Contributions of the corrections to the tetramer
ground-(excited-)state energy, -573.90 (-132.70) mK, are found to be,
respectively, -4.13 (-1.52) mK, +9.37 (+3.48) mK, -1.20 (-0.46) mK and +0.16
(+0.07) mK. Further including other realistic 4He potentials, we calculated the
binding energies of the trimer and tetramer ground and excited states, B_3^(0),
B_3^(1), B_4^(0) and B_4^(1), respectively. We found that the four kinds of the
energies for the different potentials exhibit perfect linear correlations
between any two of them over the range of binding energies relevant for 4He
atoms (namely, six types of the generalized Tjon lines are given). The
dimerlike-pair model for 4He clusters, proposed in the previous work, predicts
a simple universal relation B_4^(1)/B_2 =B_3^(0)/B_2 + 2/3, which precisely
explains the correlation between the tetramer excited-state energy and the
trimer ground-state energy, with B_2 being the dimer binding energy.
