Both Boston cream and Bavarian cream are egg custards with a smooth consistency, and both are made by mixing all their ingredients together and whisking like mad, then cooking them on medium heat while stirring continuously. So far, so same.
But the ingredients themselves present the first difference. Bavarian cream involves milk, eggs, sugar, and often vanilla extract, the same as Boston cream. But then the two ingredient lists diverge: Bavarian cream includes heavy cream and gelatin, while Boston cream involves cornstarch. Though this doesn’t have a huge impact on flavor, as both are essentially vanilla custards, the texture varies wildly. The use of heavy cream and gelatin means Bavarian cream sets more thoroughly, creating a thicker, richer consistency. Using only corn starch, meanwhile, means Boston cream is a lot runnier — but it also has an extremely silky texture that Bavarian cream can’t match.
Additionally, they’re not even eaten the same way. Bavarian cream doesn’t have to be part of a donut or a cake to be consumed; people will just eat bowls of the stuff owing to its thick yet light consistency. If someone did that with Boston cream, they would catch some very sidelong glances. (The other difference when it comes to the donuts is the toppings — Boston creams are chocolate-glazed while Bavarian creams are topped with powdered sugar — but we’re just talking about the cream here.)