The main difference is the alcohol in each cocktail. Margaritas are made with tequila and sweetened with triple sec, while daiquiris are made with white rum and simple syrup for sweetener. Their common ingredients are lime juice, lots of ice and sometimes fruit juices.
A classic Daiquiri, the Cuban cocktail that dates back to the late 1800s and was famously the drink of Hemingway (admittedly with a few tweaks), is served up, not frozen. But sometimes you yearn for something boozy and cold, authenticity be darned.
Daiquiri: Daiquiris always contain some version of fruit or citrus juice and will always have to be shaken in order to achieve the right texture and blend of flavors.