  The advent of gravitational wave (GW) and multi-messenger astronomy has
stimulated the research on the formation mechanisms of binary black holes
(BBHs) observed by LIGO/Virgo. In literature, the progenitors of these BBHs
could be stellar-origin black holes (sBHs) or primordial black holes (PBHs). In
this paper we calculate the Stochastic Gravitational-Wave Background (SGWB)
from BBHs, covering the astrophysical and primordial scenarios separately,
together with the one from binary neutron stars (BNSs). Our results indicate
that PBHs contribute a stronger SGWB than that from sBHs, and the total SGWB
from both BBHs and BNSs has a high possibility to be detected by the future
observing runs of LIGO/Virgo and LISA. On the other hand, the SGWB from BBHs
and BNSs also contributes an additional source of confusion noise to LISA's
total noise curve, and then weakens LISA's detection abilities. For instance,
the detection of massive black hole binary (MBHB) coalescences is one of the
key missions of LISA, and the largest detectable redshift of MBHB mergers can
be significantly reduced.
