Could you explain exactly HOW these [city culture and tile culture] differ (the effect on neighboring tiles from culture bombs vs growing culture organically). In mathematical terms (formulas) if possible? WHY do they differ?
The thread that Conquistador 63 links to is the place to go for a detailed explanation. I had no idea how tile culture worked until fairly recently, when I went looking for info and found that thread. Here's a very superficial and possibly inaccurate summary of Deranged Duck's post:
Every tile has the ability to hold culture from every civ in the game, simultaneously. The civ with the highest amount of culture in the tile controls the tile,
if the tile is within reach of one of its cities.
How do tiles get culture? From nearby cities. Every turn, a city will add some of its owners culture into every tile that is within its cultural radius. So for a newly established city you'll add culture to the tile it is on and the tiles immediately adjacent to it, but once you hit the first border expansion (based on total culture in the
city) you'll also add to the tiles two spaces out, and so on and so forth. This is true even for tiles that another civ currently controls because they have higher culture there.
How much culture gets added to the tiles? The base amount is the amount of culture the city is generating per turn. If your city has a large cultural radius you'll get some bonus culture added to the tiles closest to the city, every turn, that is independent of what your city generates itself.
What a Great Work apparently does is first add a bunch of culture to the city, expanding its cultural borders as appropriate. And then it causes the city to add culture to the tiles within its influence. The amount of culture added is what the city would have added to those tiles over the course of twenty turns.
This is why creating a Great Work in a newly captured city doesn't do very much. Because the culture being generated per turn in your newly captured city is
zero, and twenty turns worth of zero is still zero. Except that's not quite true. Because of the bonus culture you get regardless of your culture per turn, based purely on having large cultural borders. That still applies, and twenty turns of it gives you a moderate amount of culture in the tiles closest to the city. But that's it.
Deranged Duck points out that this system means it is to your advantage to switch to 100% culture just before setting off a Great Work. If you trigger a Great Work in a city that is currently generating hundreds of points of culture per turn then you will add twenty turns worth of that in an instant to every tile within that city's cultural reach.