Those are quasars, and they tend to be much steadier. While they’re eating, they’re generally eating from an accretion disk that’s continually falling in. There’s some variation (accretion disks can be lumpy), but they’re simply too large to get variation on the scale of seconds, like we see with GRBs.
It’s currently believed that there are two different kinds of gamma ray bursts, produced by different sources. The first are the long-duration GRBs: It’s believed that these are due to exceptionally powerful supernovae, which beam their output to seem even more powerful to something that happens to be on axis to them. The second are the short-duration GRBs, which are believed to be due to a collision of two neutron stars to form a black hole (the end of the burst is due to almost all of the material being swallowed by the hole as it forms).