The Pillars of Creation have a strong directional sense. They are referred to as "pillars" and another question asks how "tall" they are. Naively, it looks as if there is a source of "smoke" near the tips of the pillars, and the smoke is being blown by a wind. News explanations and Wikipedia explain that the pillars are formed by UV light from hot stars eroding clouds of molecular hydrogen, which suggests that the "smoke" is actually a void, but it still looks as if the void is being extended by the flow of a wind past the relevant stars.
But I have no confidence that this is right, and the Wikipedia article is not very clear. Popular media explanations also don't seem to address the geometry.
I see several possibilities:

The gas is still relative to most of the nearby stars, and a small number of hot stars are moving through that system, causing the pillars.
The hot stars are not in rapid motion relative to nearby stars, but the gas is flowing relative to that population.
The shape has nothing to do with relative flows.

What's the explanation? A pointer to a good article for the knowledgeable lay person would be helpful too.

Your option #3 is correct; the shape has little to do with the relative motion of the gas and stars.
Giant molecular clouds
The pillars are part of the giant molecular cloud (GMC) which is giving birth to news stars. Stars are formed when some regions inside the cloud meet the Jeans criterion, i.e. are sufficiently dense and cold that gravity overcomes pressure. Because the density of such clouds is largest in the center (see e.g. Chen et al. 2021), stars will tend to form first in the center.
Stars are formed with a distribution of masses. The most massive ones — the so-called O and B stars — emit copious amounts of ultraviolet photons, which heat and ionize the surrounding medium. A hot, ionized bubble inside the otherwise cold, neutral, and dusty cloud called a Strömgren sphere then forms.
The dark pillars are remainders of the neutral gas, whereas the bluish region is the ionized region, containing newborn stars.
The size of the ionized region
In this answer about the Carina Nebula, I calculated the typical size of a Strömgren sphere, which we can write approximately as
$$
R_\mathrm{S} \simeq 10\,\mathrm{lightyears} \times\color{red}{\left(\frac{Q(\mathrm{H}^0)}{10^{50}\,\mathrm{s}^{-1}}\right)^{1/3}}
\color{blue}{\left(\frac{n_\mathrm{H}}{300\,\mathrm{cm}^{-3}}\right)^{-2/3}}
\color{green}{\left(\frac{T}{10^4\,\mathrm{K}}\right)^{0.23}},
$$
where the three colored terms show typical values of the rate of emitted UV photons $\color{red}{Q(\mathrm{H}^0)}$ from a handful of massive stars, and the neutral hydrogen density $\color{blue}{n_\mathrm{H}}$ and temperature $\color{green}{T}$ of the cloud.
This equation tells you two things, namely that

the characteristic size of the ionized region is of the order of 10 lightyears, and that
the size scales with density as $R_\mathrm{S} \propto n_\mathrm{H}^{-2/3}$.

The origin of the pillar shape
But the GMC is not homogeneous; it will have regions that are quite a lot denser, and quite a lot less dense, than the average. According to point #2 above, if some region is, say, 10× more dense than its surroundings, the ionized bubble will propagate $10^{-2/3} \sim 1/5$ as far in this region. The overdensity will therefore shield the part of the cloud that is behind it from the UV radiation of the stellar cluster. This effect causes "pillars" of neutral gas to appear behind the dense regions.
In the animation below I attempt to show the evolution of the Strömgren sphere. Stars are formed first in the center, but a secondary high-density region (which perhaps is too hot to start forming its own stars) shields the gas behind it, shaping a pillar.

The image below shows you the "pillars of creation" with their surroundings, where you can see the stellar cluster in the center of the Eagle Nebula responsible for this shape:

Credit: NASA/ESA/STScI/WikiSky.
Opaqueness vs. transparency
Neutral gas is quite efficient at blocking light, because the atoms have many electronic transitions available for absorbing photons. Moreover, the gas is full of dust, which also absorbs light. In contrast, ionized gas is much less efficient at absorbing light, and moreover the dust will tend to be destroyed by the free-streaming UV radiation (sublimation from heating), and by high-temperature particles (sputtering).
(when I say "ionized gas", this means that hydrogen — which comprise ~90% of the atoms — is more or less fully ionized. But helium and heavier elements still have bound electrons which may absorb some of the light.)
Hence, the neutral regions are very opaque, while the ionized regions are transparent.
