  The newly synthesized strontium doped RNiO$_2$ (R=Nd, La) superconductors
have stimulated extensive interests in understanding their pairing mechanism
and pairing nature. Here we study the pairing mechanism in this family from a
two-orbital model comprising the Ni- $3d_{x^2-y^2}$- and $3d_{xy}$- orbitals,
equipped with extended Hubbard interactions and induced low-energy effective
superexchange interactions. We then study the pairing symmetry in this system
by using large scale variational Monte Carlo approach. Our results yield the
intraorbital $d_{x^2-y^2}$-wave singlet pairing as the leading pairing symmetry
in the nickelates, which is analogous to the cuprates. However, there exist two
important differences between the physical properties of the two families due
to the fact that at the low Sr-doping regime, while the Ni-$3d_{x^2-y^2}$
orbitals remain half-filled and singly-occupied to form a Mott-insulating
background, the Ni-$3d_{xy}$ orbitals accommodate nearly all the extra doped
holes, which move freely on this background. The first difference lies in the
single-particle aspect: while the $3d_{x^2-y^2}$ degree of freedom remains Mott
insulating with spectra weight pinned down at zero at low dopings, the
$3d_{xy}$ one behaves as Fermi liquid with spectra weight near 1. The second
difference lies in the pairing aspect: while the huge
intra-$3d_{x^2-y^2}$-orbital pairing gap is actually a pseudo gap which has
nothing to do with the SC, the small intra-$3d_{xy}$-orbital pairing gap serves
as the true superconducting pairing gap, which is related to the $T_c$ via the
BCS relation. Both differences can be verified by the angle-resolved
photo-emission spectrum.
