  [Ca$_2$CoO$_3$]$_{0.62}$[CoO$_2$], a two dimensional misfit metallic
compound, is famous for its rich phases accessed by temperature, $i.e.$ high
temperature spin-state transition, metal-insulator transition (MIT) at
intermediate temperature ($\sim$ 100 K) and low temperature spin density wave
(SDW). It enters into SDW phase below T$_{MIT}$ which becomes long range at 27
K. Information on the independent role of misfit layers (rocksalt/Ca$_2$CoO$_3$
\& triangular/CoO$_2$) in these phases is scarce. By combining a set of
complementary macroscopic (DC magnetization and resistivity) and microscopic
(neutron diffraction and X-ray absorption fine structure spectroscopy)
measurements on pure (CCO) and Tb substituted in the rocksalt layer of CCO
(CCO1), magnetic correlations in both subsystems of this misfit compound are
unraveled. CCO is found to exhibit glassiness, as well as exchange bias (EB)
effects, while CCO1 does not exhibit glassiness, albeit it shows weaker EB
effect. By combining local structure investigations from extended X-ray
absorption fine structure (EXAFS) spectroscopy and neutron diffraction results
on CCO, we confirm that the SDW arises in the CoO$_2$ layer. Our results show
that the magnetocrystalline anisotropy associated with the rocksalt layer acts
as a source of pinning, which is responsible for EB effect. Ferromagnetic
clusters in the Ca$_2$CoO$_3$ affects SDW in CoO$_2$ and ultimately glassiness
arises.
