It really does feel like the two concepts are related, but there are enough differences that you can't just say we're inside a black hole. For one thing, the inside of a cosmological horizon corresponds to the outside of a black hole. I do think the similarity is part of what drives so many physicists to study black holes and quantum gravity, though. Horizons are a consequence of dynamical spacetime, but a deeper theory is needed to see the universe and black holes as manifestations of some more primitive concept.
This is actually very similar to what I've heard an observer falling into a black hole would experience... as you fall in, space curves to bend all outward worldlines back to the singularity. You never experience the horizon itself even while passing it, but would see the horizon wrapping itself around you in all directions.
Astronomers in different galaxy clusters looking at the M87 black hole would agree within their observational abilities that there is a horizon localized deep within the visible matter of the galaxy. Astronomers will keep agreeing that into the far future.
Astronomers in different galaxy clusters will agree that each sees a set of cosmological horizons, but do not agree on where it is and what's inside it.
Schematically:
th<--g1<--<--yh--Them<--->You-->th-->g2-->yh
The gt/lt arrows represent the metric expansion in one direction; Them and You are the two respective observers' galaxy clusters. G1 and g2 are two distant galaxy clusters. Yh and th are your and their horizon, respectively. G1 is inside their horizon but has crossed yours. G2 is inside your horizon but not inside theirs.
Every point in an expanding universe has its own set of cosmological horizons non-identical to its neighbouring points, and dramatically different from points at great distances in spacetime (that goes for great gaps in time at the same spacelike location, and great gaps in space at the same lookback time or scale factor).
For astrophysical black holes, a black hole horizon localizes around a particular clump of matter, and not around other nearby clumps of matter. Far from a super-dense clump of matter you will not find an astrophysical black hole horizon (barring primordial black holes, for which there is no evidence anyway).
Cosmological horizons focus on each infinitesimally small clump of matter, everywhere in the universe, even in deep extragalactic space where matter is extremely sparse. Indeed, even matter-free points have their own cosmological horizon, and we do have substantial evidence supporting that.
A theoretical black hole horizon arises in a family of solutions of the Einstein Field Equations, from exact ones like Schwarzschild or Kerr, to solutions that become those asymptotically (in the limit as a black hole formed by gravitational collapse ages, for example -- Schwarzschild and Kerr are eternal black holes that are never in an uncollapsed state).
A cosmological horizon arises in a different family of solutions of the Einstein Field Equations, from exact ones like the de Sitter vacuum or the expanding Robertson-Walker vacuum, to solutions that become those asymptotically (these are vacuum matter-free solutions, and one can get there with a solution with matter that dilutes away over time).
The two families of solutions are very different, although there is an overlap of solutions for black holes in expanding spacetimes, where there can be both a black hole horizon (or horizons) and a cosmological one (or more than one).
We can compare these different families of solutions most strikingly using the behaviour of test particles scattered through the spacetimes: near the BH event horizon particles may be entrained into stable circular orbits around the horizon of a theoretical black hole like Schwarzschild or Kerr, whereas this never happens around a cosmological horizon in a solution like de Sitter or expanding Robertson-Walker: the test particles all plunge right through the observer's horizon radially.
Once through the BH horizon a test particle will inevitably and very quickly by its own "wristwatch" collide with the gravitational singularity after passing through extremely curved spacetime. Our galaxy cluster has already passed through many cosmological horizons centred on distant galaxies who are now outside our horizon too. Neither our galaxy cluster nor the many distant ones have changed their essentially exclusive time-like trajectories, and there is no evidence we are soon going to end up colliding with a gravitational singularity. (Current evidence doesn't suggest we are going to end up facing a big rip either).
Now, in the cosmological model under time reversal galaxy clusters do tend to converge and naively collide and collapse into a singularity eventually. However, galaxies all plunge into it radially and matter does not get entrained into any sort of accretion disc or similar structure. (They disintegrate into clouds of gas and dust that heat up into the "un-recombination" surface of ionizing atoms (mostly hydrogen) which gets denser and hotter until neutrons and protons disintegrate, electroweak symmetries emerge, and so on, all at once. Black holes usually get to swallow clumps of matter from time to time, whereas the time-reversed big bang singularity gets everything landing on it all at once, rather than some clumps early, and some clumps earlier still).
Physically realistic models built on these theoretical systems are grossly different; the models are good for predicting future things in our sky, so we expect the astrophysical reality is different too.
The rough similarities tend not to survive real inspection. Different horizons are different in a bunch of ways that aren't overcome by the few ways in which they are somewhat similar (or similar under time-reversal).
