Model/property releases and copyright ownership are two different subjects.
Model & property releases...In this example, the car owners' sign model & property releases giving the photographer the right to use the images of their cars and themselves any way they wish. Other parties featured in images also should sign releases. Best examples of model and property releases, and among the most commonly used can be found with detailed descriptions here:
https://www.asmp.org/property-model-releases/Model/property releases have little to nothing to do with copyright ownership (i.e., the topic of this post, according to its headline). Releases simply determine how an image may or may not be used. A fully and properly released image potentially has a lot more value than an unreleased image. A release might reiterate that copyright ownership remains with the photographer (or their employer), but this is merely a clarification. The copyright owner can do almost anything they wish with fully released photos. The owner can license image usage for commercial or editorial purposes, display them publicly online without restriction, use them in a portfolio and in self-promotion materials and more.
Model/property releases primary purposes are to reduce risk and discourage lawsuits. Some uses tehcnically don't require a release: news/editorial, educational, portfolio, fine art.
However in all cases it is better to have a signed release and in some cases it's become standard practice or expected. For example, more and more editorial users are asking for them (magazines, newspapers, websites, etc.)... especially for "soft news" photos. A major newspaper I worked for some years ago had something like active 50 court cases on any given day. Of course, not all those were related to images they'd used... but some were. Anything they could do to reduce that number of court cases and legal costs that come with them was helpful.
There are some image types and usages where a standard release might not be sufficient... Such as nude photos or defamatory uses. A more explicit model/property release, identification and proof of age may be necessary for a photog and/or their employer to CYA. Not likely to be needed at a car show... But, hey, who knows!
Copyright ownership...There are situations where a photographer may not own the copyright of images they take. The primary situation where that occurs is "work for hire". This is where the photographer is a "regular employee" such as a staff photographer for a newspaper or magazine. A friend of mine was an Associated Press photographer for ten years, early in his career. All the images he took as part of his job during that time period are owned by AP... not by him. He's actually bought usage some of his own images as stock photos, when AP has offered them for sale.
Another photographer I worked with years ago took one of the most iconic news photos of the 20th century while employed as a staff photographer by the Dallas Morning News. He won a Pulitzer, but the newspaper owned the copyright and sold usage of the image widely for many years. When the photographer retired, the newspaper gifted the copyright of the image to him. He has been able to license it's usage many times since then.
In the case given above, the VFW just paying the photographer $1 would not constitute "work for hire" very clearly. In the case of a temporary hire such as that implies, work for hire must be clearly defined in a written agreement signed by both parties....
in the United States. It may be different in other countries. For example, I don't know that it's true, but I've been told that it's just the opposite in Italy... that any sort of payment (such as the fee paid to a wedding photographer) automatically makes it work for hire, unless it's in writing that it is not.
The situation where the VFW paid the photographer $1 is a good example of why it's important that a written agreement be signed by both parties, to fully clarify each party's duties and to definitively spell out who owns the images being made. If there's no written agreement and the VFW chose to dispute it, they might take the photographer to court over copyright ownership... claiming it was work for hire because they paid them $1. In a U.S. court, chances are the photographer would win the case. However, even so they would have hefty legal bills. Even winners in court sometimes end up bankrupted by the costs of defending themselves!
Ask a lawyer to be certain. I'm just a photographer who has to deal with some of this stuff!