When ordering a Daiquiri, like when ordering a Martini or even a steak, you need to convey exactly what Daiquiri you desire and how you'd like it. It's essential to be specific as ordering just a "Daiquiri" could result in your being asked, "What flavour would you like - strawberry, banana, mango or pineapple?" In such cases answering, "just lime please" often leaves the questioner perplexed.
When I first visited Cuba back in the late 1990s, I learned that asking for a mere "Daiquiri" (pronounced 'Dye-Ker-Ree') would result in my being served a blended slushy Daiquiri, the default serve for a Daiquiri on this hot island. I quickly learnt that, at that time in Cuba, you needed to order a "Natural Daiquiri" when seeking a classic shaken rather than blended Daiquiri.
Constantino (Constante) Ribalagua Vert, the bartender who presided over the bar at Havana's La Florida (later renamed Floridita) in Havana for some 40 years, until his death in early December 1952, is credited for making the frozen Daiquiri famous. He also further confused ordering a Daiquiri by listing his Daiquiri adaptations by number - presumably in the order he created them: Daiquiri No.2, No.3, No.4 and No.5.
Thus, an "original"/"classic" Daiquiri should properly be termed Daiquiri No.1 and this can be served either 'natural' (straight-up), 'on-the-rocks' (over cubed ice) or 'frozen' (blended with crushed ice).