Homemade Sausage Making

This is not an idle or trick question because I believe that the term anerobic means an absense of oxygen.
My smoker as it is built and used has several holes open to the air to supply air to the grill burner. My smoke is generated remotely in a separate fire chamber.
I often have a gas flame heating the smoker to cook the meat to temperatures above the outside air temperature. Small flames are sometimes a problem for me because the wind blows them out.
I use and will continue to use sodium nitrite in my cures because it is called for and I like the taste it imparts.
Do the more enclosed smokers with the smoke generators inside and the ability to close the dampers make the distinction?

Your definition is correct, and in reference to anaerobic bacteria, like C. botulinum, that's what it means - no oxygen. Your smoker is never truly anaerobic, but heated, it does become a low-oxygen environment above the heat source. It isn't the smoker that has to be anaerobic for botulism to spread. The only anaerobic environment that matters is the micro-environment immediately surrounding the spores, which could be inside a sausage, or a canning jar, or inside a cut in a whole muscle meat, or under loose skin, between flesh and bone, along connective tissue between muscles, or in a remote spot inside a cavity, such as the body cavity of a fish being smoked or a puncture in muscle. The micro-environment that has to be anaerobic is so small that it isn't even observable, so it takes very little space without oxygen for the spores to proliferate if the pH, temperature, salt content and water activity are also within limits.

In the case of vegetative forms of C. botulinum, they infect cells and have an anaerobic environment inside the cells, where they proliferate and produce toxin until the cell ruptures and the toxin is spread.

Here is a detailed discussion about C. botulinum.

Thanks Tom. I know that it doesn't take much to kill and it isn't a pleasant manner of death.

A lethal dose for an adult is about one microgram of toxin. When it is so easy to avoid, by proper hygiene and food safety practices, and the use of potassium or sodium nitrate/nitrite in cured sausages and whole muscle meats, and when we know that very little of the nitrate/nitrite remains in the end product, it makes no sense to take the risk of shortcuts in proper handling, or failing to use the most effective method of protecting against C. botulinum.

All of which begs another question. More and more often the meat offered in the grocery stores has been pumped. no one doubts the high bacteria counts on the outside of the meat. Using the same needles on countless pieces contaminates them all. This makes safe handling even more critical. I can't recall seeing nitrites included in the soup used to pump the meat so is refrigeration the only barrier to the growth of C.Botulinium?