Perhaps the best place to start in the discussion of what makes a watch "casual" is the case material. Stainless steel (normally 316L, which is a surgical-grade, hypoallergenic steel) is by far and away the most common material used for casual watches. It is increasingly common to see this steel plated with either PVD (Powder Vapor Deposition), DLC (Diamond-Like Carbon), or IP (Ion Plating) to change its surface color (normally black, but other colors are possible too).
Plastics are also very common in casual watches. This material allows for a wide array of colorful, fun and durable pieces. Brands like Swatch and Casio excel in producing this style of casual watch.
While more unusual materials like carbon fiber, titanium, and ceramic can certainly be used in watches of a casual style, their implied dynamism (derived from their many, more ubiquitous, high-tech applications) would make them more likely to feature in watches designed to be sporty.
It would be very unusual to encounter a watch made from precious metals being described as casual. While there are some exceptions that can be found coated in a material resembling a precious metal (like a rose or yellow gold PVD coating), such a surface finish would suggest the watch was intended to be a dressier piece rather than a casual watch.
Generally speaking, there is little consistency in sizing for casual watches. Metal watches tend to be larger, while plastic watches can be much smaller, often with an emphasis on colorful design. However, these characteristics are not universal by any means.
Luxury watch collecting can be an intimidating business from the outside looking in. Meanwhile, the casual watch genre is not the place to find high-end finishing, artisanal arts or crafts, or luxury stone set cases. Rather, this category is for fun and is an excellent entry-point for younger or newer fans of watchmaking. Certain brands are at once affordable, credible, and expressive. Brands like Tissot, Hamilton, and Swatch (all owned by the Swatch Group) all offer a wide range of laid back or exciting styles that have the look and feel of a very accomplished piece. These "gateway" models are essential to continuing the passion for watchmaking into future generations.
The Casio G-shock range is a great example of the casual watch. The range is not only eminently affordable, but also incredibly collectible. Lots of long-time collectors of serious watches have one or two Casio watches in their collection. This is because Casio watches are well made, well designed, and offer a colorful and fun aesthetic, often commemorating an artistic partnership or special event.