I think dpwilson's answer is excellent and I voted him up, but I wanted to post this chart with the old picture is worth a thousand words point of view.
Venus is somewhat lighter then Earth, yet has a much thicker
atmosphere. One would imagine that the following should be true:
During the formation phase, all inner planets had captured as much gas
as they could hold per gravitational/thermodynamic equilibrium. After
all, even puny Mars managed to capture a sizable atmosphere.
Maybe. But during the early solar system, once the sun has formed and starts pumping out light and solar flares, (and the early sun was likely much more active in shooting out solar flares in part due to a faster rotation), a key factor to consider is the Frost Line - which is well past earth.
So, 1 of 2 things can happen in the early formation of the Solar-system. One, the planets form and collect available ices and gas they can before the sun starts melting/pushing away any ice and gas inside the frost line, or 2, the sun forms first and the inner planets have very little gas and water as they form. They do get bombarded by hydrogen ejected from the sun, but mostly the inner planets aren't good at holding onto this hydrogen. In the 2nd scenario, any atmosphere and water they get would have to come from comet impacts.
The early atmosphere of the inner planets were mostly CO2, CH4, NH3 maybe some N2. If Venus was struck by a couple extra comets, that alone would explain it and it's not statistically unreasonable. Now, I'm not saying this is what happened, only that it's possible. Venus retains most of it's CO2, but it could lose over time most of it's H20, CH3, NH3, maybe N2 if it was present, leading to the mostly CO2 atmosphere it has today.
It's also theoretically possible that the giant impact that formed the moon also blew away a lot of Earth's early atmosphere. (not certain of that but the enormous addition of heat and rotation, it's possible).
In the chart above, it suggests Venus won't lose much H20, but other charts have Venus closer to the H20 line. (google gas escape velocity planets for more charts)
The rate of atmospheric escape should be much higher for Venus: Venus
receives more heat from the sun, thus higher Jeans escape rate Venus
has negligible magnetic field, so some of its atmosphere must be lost
to direct "blow-off" by solar wind
This is true. It might well explain why Venus has so little water which is common in the solar-system. But on your last point, Venus has an induced magnetic field - see here. dpwilson explained this in more detail.
Yet, it is Earth that seemingly misses a great deal of atmospheric
volume. So the question is: what are the current theories regarding
the "thinning" of the Earthian atmosphere? When and why the
atmospheric gases had left the planet?
I gather there's still come uncertainty on precisely what Earth's atmosphere was like billions of years ago. It might well have started out with an even denser atmosphere than Venus currently has, but it's hard to know with any certainty (at least, nothing I've read suggests certainty on the subject).
It's worth pointing out that coal, oil and natural gas don't form naturally, but they are the product of dead plants and sea life buried over hundreds of millions of years. Also, many of the rocks we see all around us have Oxygen in them. Granite has Oxygen, for example. (There's no, or at least, very little Granite on Venus). The absorption of atmosphere by life on earth and by Oxygen binding to surface and dissolved ocean minerals likely played an enormous role in thinning out Earth's atmosphere. Life on earth, all by itself, could be enough explain the difference in Earth's to Venus' atmosphere.
1) Comets used to be larger. Every pass near the sun, comets shrink. Besides, it's not just comets it's icey moon like objects and asteroids, which, as Jupiter migrated and the late heavy bombardment took place, some of those could have been quite large.
See: Here and Here and Here.
Besides, I didn't say it as definitive, I said it was possible a large part of Venus' atmosphere came from a large comet strike.