The card logo I would date it to the late 40s early 50s, but these companies may keep the same logo for decades. The button style is more early 1950s.
There was a lot of experimentation in the 1940s and 50s with what we would today call 'plastic'. Many different formulas and techniques. What I am saying is: Lucite or Bakelite are pretty much specific recipes, like Pot Roast or Spaghetti Sauce, where as "Plastic" covers a whole range of different combinations of polymers, like saying "cake" without defining the kind of cake. there are millions. The makers of these plastics rarely had a trade name and may only provide a name in their patent application, like "poly-handrocyldric formula with Cloride-saturate properties"; to the manufactures of buttons they sold the formula as "a new kind of plastic" or maybe "Self Coloring Plastic". Often the differences in these polymers was very slight. Many of the raw materials were created by one company, like Dow, the manufacturers experimenting with the raw material. "Plastic" is probably the best term, unless you want to do 40 years of research with a team of 12 to define every slight variation of plastic made at the time.
Personally I group the various types as:
Hard plastic, like your button
Squirt-gun Plastic, a brittle plastic usually transparent
Vinyl, slightly flexible, sometimes becomes a little brittle with age.
Asphalt plastic, an imitation bakelite, like rubber it becomes crumbly or brittle with age, usually in a dense opaque color.
Again, these are catagories, not specific recipes.
Buttons can be a fascinating hobby, but can be frustrating too. Sorting buttons was about the only thing I could do for hours and not get bored to death.
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