Centuries ago, cooks started pureeing almonds with sugar to make almond paste and marzipan to add a nutty sweetness to baked goods, and although they may seem identical, these culinary cousins have vastly different jobs. Almond paste is almonds and sugar ground into a soft, moist, and gritty paste and often includes a bit of egg white to help bind the mixture. 

Marzipan is, essentially, almond paste with extra sugar, egg whites, and almond extract, which minimizes the almond flavor while stabilizing the mixture, adding the perfect pliability for food sculpture. Food & Wine calls marzipan “the original fondant,” as it can be rolled into sheets and used to cover cakes, but it’s probably best known for being sculpted into fruit and vegetable candies.

However, almond paste isn’t smooth enough to be sculpted and won’t hold a shape, but the egg omission means that almond paste is supremely almond focused. Per Food & Wine, the two are not interchangeable. So, if a recipe calls for almond paste, you can't sub in marzipan, but "you can turn almond paste into marzipan by adding some sugar and egg whites." 

Although marzipan's smooth texture is harder to make, both can be made with a food processor, but BBC goodfood has a recipe with a great shelf life, stating, "Although homemade marzipan contains raw eggs, the amount of sugar, and lack of moisture, prevents bacteria growing when left at room temperature, so your cake should last for 1-2 months iced."