The history of custard is likewise ancient. This food followed a separate, though parallel, path that managed to converge with pudding in 19th century America.
Food historians generally agree the first puddings made by ancient cooks produced foods similar to sausages. The British claim pudding as part of their culinary heritage. Medieval puddings (black and white) were still mostly meat-based. 17th century English puddings were either savory (meat-based) or sweet (flour, nuts & sugar) and were typically boiled in special pudding bags. The “pease porridge” most of us know from the old nursery rhyme was most likely a simple boiled pudding of pease meal. By the latter half 18th century traditional English puddings no longer included meat. 19th century puddings were still boiled but the finished product was more like cake. These puddings are still traditionally served at Christmas time. Plum pudding (aka Christmas pudding) is a prime example. Modern steamed puddings descend from this tradition.
About custard? Ancient Roman cooks recognized the binding properties of eggs. They were experts at creating several egg-based dishes, most notably patinae, crustades and omlettes. These foods were either savory (made with cheese, meat, pepper etc.) or sweet (flavored with honey, nuts, cinnamon etc.). Food historians generally agree that custard, the sweet almost pudding-like substance we know today, dates to the Middle Ages. At that time custard was eaten alone or used as fillings for pies, tarts, pastry, etc. Flan is probably the most famous and widely adapted custard dessert in the world. It is important to note that custard was not unique to Europe. Similar recipes flourished in Asia.
The distinction between European custard and American pudding became muddled sometime in the 1840s. At that time in America, traditional boiled puddings were no longer necessary to feed the average family. There was plenty of food. This also happened to be the same time when Alfred Bird, an English chemist, introduced custard powder as an alternative to egg thickeners. It wasn’t long before Americans began using custard powder and other corn starch derivatives as thickeners for custard-type desserts. This proved quite useful for overlander (conestoga wagon) cooks who did not have ready access to a reliable supply of fresh eggs.

Chocolate pudding & custard
The earliest print reference we find for chocolate pudding is 1730. Chocolate custard, a thick creamy cousin, dates to the 19th century. These sweets were enjoyed by wealthy people. In the last decades of the 19th century some American social reformers and food companies endeavoured to promote these products as health food. American custards and puddings converged and were thusly marketed for their nutritional benevolence with special emphasis on invalids and children.

Some pudding-type foods have been considered healthy since ancient times. Case in point: rice pudding. This ancient recipe was traditionally prescribed for the young and infirm. The formulae were inscribed in medical texts before the showed up in cookbooks. Tapioca, arrowroot, and corn starch puddings (made from new world thickeners) were also recommended as restoratives.