Does horchata contain milk?

The recipes below don't have 'milk'. The method gives the idea that there is milk. See below;

..........

Horchata (Cinnamon Rice Milk)

INGREDIENTS

1 cup long grain rice, rinsed

2 quarts water

1 cinnamon stick, broken into pieces

1 teaspoon vanilla (optional)

1/2 cup white sugar

DIRECTIONS

In a large saucepan, combine rice, water and cinnamon stick. Set aside for 3 hours.

After 3 hours, bring to a boil, reduce heat, and simmer for 30 minutes. Allow to cool.

Puree rice mixture in a blender until smooth. Strain through cheesecloth or a fine sieve. Flavor with vanilla and sugar to taste. Chill, and serve over ice.

http://allrecipes.com/Recipe/Horchata-Cinnamon-Ric...

........

Horchata

Horchata is an old-world drink that was enjoyed by the Aztecs. Today this agua fresca is served throughout Mexico, as well as in many authentic Mexican restaurants in the United States. Horchata is a cool and soothing enhancement to spicy food.

1 cup uncooked white rice

1/4 cup ground, blanched almonds or almond meal

1 cinnamon stick

6 cups water, divided

1/2 teaspoon vanilla extract

1/2 cup sugar

Put the rice in a blender and grind to a powder (about 2-3 minutes). You can also use a spice grinder or coffee grinder for this. Grind the mixture as smooth as possible. Combine the pulverized rice, ground almonds and cinnamon stick. Cover tightly and allow to set overnight or at least 6 hours.

Remove the cinnamon stick and place the rice mixture in the blender. Blend for 4 or 5 minutes until the mixture is smooth, powdery and no longer has a gritty texture. Add 2 cups of water, and blend again for about 15 seconds.

Strain into a pitcher through several layers of dampened cheesecloth (or a coffee filter). Do not skip this step or the drink will have a chalky taste.

Add 4 more cups water and the vanilla and sugar, stirring until the sugar dissolves. If the mixture is too thick, add some additional water. Horchata should have the consistency of milk. The drink is supposed to be sweet, so taste and add more sugar, if desired.

Cover and refrigerate. Horchata will keep several days, refrigerated. Serve it chilled in tall glasses over ice. Makes 1-1/2 quarts.

http://www.texascooking.com/recipes/horchata.htm

.....

Add 4 more cups water and the vanilla and sugar, stirring until the sugar dissolves. If the mixture is too thick, add some additional water. Horchata should have the consistency of milk. The drink is supposed to be sweet, so taste and add more sugar, if desired.

if it tasted like milk, it probably had milk. but why they added milk, it's beyond me.