Short answer: They're probably not safe.
Unlike "microwave safety", there isn't a safety risk in contaminating the food contents of the jars due to heating in an oven; in this case you just run the risk of the jars breaking.
I am not sure what the symbols on the bottom of your jar mean; (see edit below) from what I understand—unlike plastic resin identification codes—there isn't a standard set of symbols for glass. Those symbols likely represent the manufacturer, production date, and patents.
Unless glass is processed in a special way, it is prone to breaking when it goes through rapid temperature changes. Therefore, if your glass is run-of-the-mill soda-lime glass (which is extremely likely), and if you were to put it from room temperature directly into a 450°F oven, the shock of that rapid temperature change would likely crack it. Furthermore, even if you were able to gradually heat it up to 450°F without it cracking, it would likely crack even as it naturally cools down. In order to try and ensure that the glass doesn't crack you'd have to both gradually heat the jars up and then very gradually step the oven temperature back down to room temperature.
If you want to use glass, your best bet would be to use something like Pyrex.
Even Pyrex, which is explicitly designed to be oven safe, can't withstand the direct heat of a broiler, though.
Edit: I believe the symbol on the bottom of your jars reads "A.G.C." surrounded by the outline of the state of Arkansas. This implies that your jars were made by the Arkansas Glass Container Company. I believe the numbers indicate the model number, which appears to be this jar. AGC unfortunately don't have anything on their website listing the oven safety of their glass. If you're really interested, you could try contacting the manufacturer.
While you are correct about the basics - both a grill and an oven can roast and sear, and it doesn't really matter if the heat comes from above or below.
However, there's some subtle details:
An oven will have fine temperature control (via a thermostat).
With an outdoor grill you can impart smoke-flavors (either via
smoldering hardwood, or by burning drippings). While that's possible
with an oven, unless you have one SERIOUSLY good ventilation-system,
you shouldn't even try it.
Grills also have the advantage of being outside - cookouts are much
less fun when you and your friends are standing in your kitchen,
staring at your oven.
Best Answer
Hello Justin,
First of all, a question like this should be answered by an expert in materials science, and I’m not. Bear that in mind when you read the following.
Generally, you should not take it for granted that coffee mugs are oven safe. Quite simply, some are and some are not.
However, high quality coffee mugs produced for the catering industry; especially the white ones with no decor, are normally oven safe. Nevertheless, I will not give you any guarantee.
Basically, coffee mugs cannot be regarded as oven safe, unless the manufacturer have stated so with a stamp underneath or otherwise have published some kind of guarantee, and the manufacturer is a respected and well-known entity within the industry.
Why coffee mugs aren’t always oven safe
A coffee mug isn’t always what it seems. Coffee mugs come in many varieties, are made from different materials, differ in decoration, and so on.
Moreover, coffee, tea, hot chocolate, and other hot drinks commonly served in mugs, are seldom; read never, served at temperatures above 100 ºC / 212 ºF. However, due to competition, special on sale items, and so on, coffee mugs of low quality might not be able to withstand temperatures much higher than this. The reason is simply that manufacturers, or the manufacturers’ customers, want to save a few pennies to gain a market advantage. There might also be a consumer demand for cheap low quality coffee mugs.
Materials
Most coffee mugs are made from some kind of ceramic. Others are made from wood, plastic, clay, pewter, steel, and a long list of other materials. Obviously, some of these materials will never be reckoned as oven safe. To keep it simple, I’ll stick to ceramic for the reminding part of this answer, although other materials might be oven safe.
Ceramics commonly found in a kitchen environment include Earthenware, Stoneware, Porcelain, and Bone china. Of these Earthenware and Bone china are seldom, read never, reckoned as oven safe, although this isn’t completely true as far as Bone china is concerned. Nevertheless, only a complete idiot would use a Bone china mug to make French Onion soup au gratin, cup cakes or any other kind of food.
That leaves us with Stoneware and Porcelain. Both Stoneware and porcelain are normally oven safe, unless decor elements have been added after the finale glaze is applied and the coffee mug is baked in a furnace.
One final remark needs to be added about coffee mugs made out of thin porcelain. Although these mugs might very well withstand the heat, it’s advisable to ensure that they are not exposed to any other kind of force while hot, e.g. handled without care.
Further information about Coffee Mugs, and links to other resources, can be found at Wikipedia: Coffee Mug.