Let me see if I can get you straight on a lot of things.
Mainly the terms being tossed around can get really confusing if you don't know the proper terminology and how to understand what generally can be considered slang.
Bullion, has
no mint mark. Is NOT available from the US Mint in any way shape or form. It's only able to be purchased by buyers in the authorized purchasers program, and even then only in boxes of 500 (monster boxes). The buyer can then sell as they please, individual or the whole box. The best bet is to refer to bullion as "bullion".
The slang is to call them uncirculated. No
ASE is intended to be "circulated", even though they have a $1 denomination. So it's a bit of a misnomer. But hold on tight, it gets worse.
In 2006 (the 20th anniversary of the American Eagle program), a new collector version was added to the program (both silver and gold eagles), the "Uncirculated" silver and gold eagle. Though they are handled better, etc than the bullion version, they have generally the same appearance as the bullion, which is another slang term you see, "burnished". The "uncirculated" term becomes the most confusing part as well as burnished.
The "Uncirculated" the true US Mint "Uncirculated" that was released in 2006 DOES have a mint mark, and IS released to the public individually the same way the Proof version is. That is key to know. Mint mark and sold individual in a capsule, box, and COA, just like a Proof.
Added note the Proof wasn't made in 2009, the Mint was having programs keeping up with demand because the economy was in the dumpster and people were investing in metals.
The true Uncirculated wasn't made in 2009 or 2010.
The one you have in the green box wasn't issued by the mint that way, someone after the mint put it in the capsule, box, and provided the COA, the only thing from the mint is the
ASE itself.
The comment about the different mints.
As I said no bullion has a mint mark, this has nothing to do with Philadelphia coins generally not having a mint mark.
From the start the San Francisco mint was making all ASEs. Within a couple years West Point started producing
ASE bullion, actually taking over all bullion by 1999. Since then West Point has made most
ASE bullion. San Francisco and Philly have made some, not many,though. At different times, all 3 of these have made proof versions. Denver has never produced a silver eagle.
All "Uncirculated" have all been West Point, except for a special 5 coin 25th anniversary set in 2011 which has a San Francisco Uncirculated, and that was the only way to get that one.
Well as usual I've gone on and on, hope this helps and ask if you have other questions.
I stick to OGP silver eagles also, I don't get in to the graded stuff.