and Cordials
Is there a difference between a liqueur and a cordial?  Nope.  The terms are synonymous.  So, since the term "liqueur" is more often used, that's the one I'll use from now on.
A liqueur is "an alcoholic beverage prepared by combining various neutral spirits (rum, brandy, gin, whiskey, and other distilled spirits) with certain flavoring materials, and containing more than 2.5% by weight of sugar syrup." *  In a word, liqueurs are sweet.  Most liqueurs have far more than 2.5% sugar syrup just to make them sweeter which, as we know, makes human beings go absolutely bonkers for them.  Liqueurs are quite popular with younger drinkers and casual drinkers, as the sweetness disguises the "taste" of alcohol.  Liqueurs are, more often than not, lower in proof than other liquors.  They are also often used in mixed drinks to give the other liquor the "flavoring" of the drink.
Liqueurs come in so many different flavors that it's probably impossible to keep up on them all.  But, let's see if I can guide you through the world of liqueurs a bit:
and Cordials
AMARETTO:  Thick, dark almond-flavored liqueur.

ANISETTE:  Flavored with anis (which tastes like black licorice).

CHERRY LIQUEUR:  Flavored by small wild black cherries.

COFFEE LIQUEUR:  Flavored by coffee beans and strictly coffee in taste.  (examples:  Kahlua, Kapali, and Kamora)

CREME DE BANANA: Flavored by bananas and yellow in color.

CREME DE CACAO:  Chocolate-flavored liqueur that comes in "white" (or clear) and "dark" (or brown) form.

CREME DE CASSIS:  Flavored primarily from black currants.

CREME DE FRAISES:  Flavored by strawberries.

CREME DE FRAMBOISES:  Flavored by raspberries.  (examples:  Chambord, Chateau Monet)

CREME DE MENTHE:  Flavored by mints (primarily peppermint) and available in "white" (or clear) and "dark" (or green) form.  The only difference being that the green has a harmless dye added.

CURACAO:  (often pronounced "Cure-uh-so")  Flavored by the dried peels of oranges.  It is a heavy orange liqueur that is available in an amber, "Orange" form and deep "Blue" form.

IRISH CREAM:  Made with Irish Whiskey and rich cream.

KIRSCHWASSER:  A high-proofed, clear, cherry brandy.

LIMONCELLO:  An Italian liqueur flavored by lemons.  A hazy, yellow color.

OUZO:  An anis-flavored liqueur from Greece.  (anis tastes like black licorice, remember)

PARFAIT AMOUR: Purple liqueur made from lemon, citron, coriander, sugar, and alcohol.

PEACH LIQUEUR:  Flavored with peaches.

PEPPERMINT SCHNAPPS: A mint liqueur, but far lighter in body than Creme De Menthe.

ROCK AND RYE:  A rye whiskey-based liqueur, but includes neutral spirits, rock candy syrup, and fruits.

SLOE GIN:  Flavored by the sloe berry (blackthorn bush).

TRIPLE SEC:  An orange liqueur much lighter in body to Curacao and of lower proof.  Often used as an ingredient in margarita.
Absente:  A legal form of "absinthe" that does not include wormwood.  UPDATE: Absinthe is back with wormwood & widely available

Baileys:  One of the finest, most popular Irish Creams (see Irish Cream above).

Benedictine:  One of the oldest liqueurs (originally produced in 1510) with a heavily guarded secret recipe.  Flavored with (but not limited to) cardamom, cloves, nutmeg and vanilla.

B & B:  also known as  Benedictine and Brandy, it is Benedictine (see above) blended with cognac.

Bols:  Liquor-producing company known for its array of liquers.

Campari:  Flavored with fruits, spices, herbs, and roots.  Red in color.

Carolans:  A cheaper Irish Cream alternative.

Chambord:  A fine, raspberry liqueur (or creme de framboises) dark in color.

Cherry Heering: Considered one of the finest cherry liqueurs, named after its founder, Peter Heering (which it, too, can be named).

Cointreau:  A fine, orange and brandy liqueur often put in place of triple sec.

Dekuyper:  Liquor-producing company known for its array of liqueurs.

Disarrono:  One of the finest amarettos (see Amaretto above).

Drambuie:  Made with Scotch malt whiskies that are, at least, 15 yrs. old and flavored with heather honey and a secret blend of herbs.

Frangelico:   A fine, hazelnut liqueur

Galliano:  An Italian liqueur flavored with a cornucopia of ingredients including anise, juniper, lavender, and vanilla.

Godiva:  The famous chocolate company's liqueurs (available in dark and white chocolate flavors).

Goldschlager:  Clear, cinammon liqueur with bits of 14K gold floating in it.

Grand Marnier:  A fine, orange and cognac liqueur (much like Cointreau).

Jagermeister:  German liqueur flavored with citrus, ginger, and licorice.

Kahlua:  One of the most popular coffee liqueurs, imported from Mexico.

Midori:  A fine, honeydew melon liqueur

Pernod: A legal form of "absinthe" that does not include wormwood.

Rumple Minze:  A fine, 100-proof peppermint schnapps  (see Peppermint Schnappsabove)

Tequila Rose:  A strawberry cream liqueur.  (Looks like Pepto Bismol).

Tia Maria:  A fine coffee liqueur (slightly more expensive than Kahlua).

Vermeer:  A new, dutch chocolate cream liqueur.
Now, perhaps you have a recipe that calls for a brand name...and you have no idea what kind of liqueur it is.  Well, here is a list of popular liqueur brand names and a brief description of what they are:
Good luck with your adventures in the world of liqueurs.  It is a complex, confusing, and often dangerous world to be in...but I think you can manage.