Wherever you are in the world, when ordering a Daiquiri you need to convey to the bartender exactly what Daiquiri you desire. It is essential to be specific otherwise 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.
I first visited Cuba with my friend Jamie Terrell back in the days when he was working behind the stick at London's Atlantic Bar & Grill. Fortunately, Jamie speaks reasonable Spanish thanks to a sun-drenched season bartending on the Costa del Sol, so as we toured Havana's bars in search of the perfect Daiquiri we were able to question the bartenders. Our first lesson was that asking for a mere "Daiquiri" (pronounced 'Dye-Ker-Ree') would result in our being handed a blended Daiquiri. We quickly learnt that at that time in Cuba you need to ask for a "Natural Daiquiri" when seeking a 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, Cuba for some 40 years until his death in early December 1952 is credited for first serving a frozen Daiquiri and making the famous. He 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).
Quick links to classic Daiquiri recipes
Daiquiri No.1 Natural (Difford's 10:3:2 formula)
Daiquiri No.1 Natural (Embury's 8:2:1 formula)
Daiquiri No.1 Natural ('countdown' 3:2:1 formula)
Daiquiri No.1 On-the-rocks (Difford's 10:3:2 formula)
Daiquiri No.1 Frozen (Difford's 16:6:6:1 formula)
Daiquiri No.1 (El Floridita style)
Daiquiri No.2 with triple sec and orange juice
Daiquiri No.2 (El Floridita style) with sweet vermouth, white cacao and grenadine
Daiquiri No.3 - with grapefruit and maraschino liqueur
Daiquiri No.4 (Florida style) - golden rum based with maraschino liqueur
Daiquiri No.5 (Pink Daiquiri) - with pomegranate syrup and maraschino
Hemingway Special Daiquiri (Papa Doble) - double the rum with grapefruit and maraschino
Mulata Daiquiri - with aged rum and originally Bacardi Elixir - now with crème de cacao