Custard and Ice Cream are marketing terms. As early as 1907, definitive explanations were published. At that time, all frozen dairy products were manufactured by swirling chilled (-5F) brine (saturated salt water) around sealed cans (with enclosed dashers) that contained the FDD (Frozen Dairy Dessert) mixture. This mix (still called that today) contained various amounts of milk and milkfat (cream) and flavorings. Because it took about 45 minutes to hand crank a quarts worth of ingredients into something resembling soft ice cream (because the chilled salt water didn't remove the heat existing in the ingredient can very efficiently), ice cream became the rarest and most prized dessert, ever.
These 1907 definitions establish unflavored Frozen Custard mix as milk and eggfat (properly cooked egg and sugar mixture), only! The natural coagulant in egg yolks helped to solidify the FDD (less cranking) and egg fat costs less than 15% of what cream cost. Unflavored ice cream mix contains milk, cream and sugar. Commercially (still less than 20% of all ice cream consumed in America), other ingredients (meant to help partially solidify the FDD necessary because brine chilling methods were so inefficient) are added. These additives were most usually flour or Gelatine (made from dried oxblood).
By 1909, the market for commercial manufacture of ice cream had developed to the point that a young inventor (working in his family's machine shop) had developed a continuous ice cream machine that used gas compression to remove the heat from the cream mixture. This revolutionary design was not patented (not only young but innocent, too) and was therefore stolen by many foundries wishing to offer this "remarkable new device" to the world.
By 1912, these definitions were no longer firm because ice cream was becoming more often made commercially (in 40 qt. sealed containers turned within brine chilled wooden tubs) than by individuals at family gatherings. When something becomes commercial, the ingredient list goes from "what would I most like to wow my family with?" to "what cheap replacements can we find that people are willing to pay for?". The costly, new-fangled, continuous, compression freezer wouldn't be accepted as "the standard" until 1929 when "improvements" allowed dairies to increase output by 50+% (at no extra cost) by tripling the air content. This left customers unsatisfied, so, for a while the butterfat (cream) was doubled until complaints ceased and the market "shook out" along price guidelines.
Most companies today are still trying to find how out much less you will accept in your FDD. Only Weber's standards, ingredients and flavorings have remained the same for the last 85 years.