Different kinds of truffle exist, but just a few have a gastronomic interest.
Only nine varieties are sold in France, and in the USA we won't see more than 4 or 5 kinds of European truffles.

Black Winter Truffle

The black winter truffle (Tuber Melanosporum), also called the "Périgord" truffle (not a trade name but only a qualification of a kind), is one of the most prestigious truffles: we call it the "Black Diamond of Provence".

More or less of a round shape, the truffle can go up to the size of an apple and even bigger, but usually weights around 2-3oz. Its skin has a pyramidal scale and its flesh goes from grayish to black with thin white veins when mature. A good truffle should be firm and have a black flesh with thin white veins.

The largest production of truffles comes from the South East of France: in Provence. The biggest truffle market takes place in a small village called Richerenches, in Northern Vaucluse: more than a ton of truffles can be traded there in one day! Truffles can also be found in Spain and Italy.
The season starts in December till March.
White Truffle from Alba

The white italian truffle (Tuber Magnatum Pico) is also called "Piémont" truffle or white truffle from Alba.

It has a smooth yellowish color skin. Its flesh goes from white to fawn-colored with white veins. It has a bit of a garlic-challot flavor.

It likes humidity and grows mostly in Northern and central Italy and a bit in Croatia.
The season goes from October to December.
Black Summer Truffle

The black summer truffle (Tuber Aestivum) is also called "Truffe de la St-Jean".

It looks like the black winter truffle, if not usually bigger and tougher. Its flesh goes from yellowish to grayish, also with white veins. Best if used fresh.

It grows in the same fields as the black winter truffle. Also grows in Spain and Italy.
The season starts in May till August, depending on the weather conditions.
Tuber Brumale

The "Brumale truffle" (Tuber Brumale) is also called "Truffe Musquée".

It's usually never bigger than an egg. Compared to the Melanosporum, its skin is never reddish before it reaches maturity. Its skin peels off easily when brushed. The flesh is dark grayish when mature with white veins, bigger than the Melanosporum.

Grows in the same fields as the Tuber Melanosporum.
Same season as the Melanosporum.
Truffe de Bourgogne
Burgundy truffle (Tuber Uncinatum) is also called "Truffe Grise".

Very close to the summer truffle, its shape is more often round. The skin is similar to the summer truffle one, and its flesh when mature is a chocolate color with white veins.

As its name says, this truffle mostly grows in Burgundy, but can also be found in Champagne, Lorraine and Franche Comté.
The season goes from September to January.
Truffe Mesenterique
Truffe Mesentérique (Tuber Mesentericum).

Very dark skin and small size truffle.

Its smell is strong with a touch of phenol.

It has no gastronomic interest.  
truffe Chinoise

Chinese Truffle (Tuber Indicum).

As the Melanosporum its skin is reddish before becoming brown-black when mature. The flesh is black with white veins and has a elasticized consistency. This truffle looks a lot like the Melanosporum but has no taste at all!

Grows in China in the provinces of Sichuan and Yunnan.

Same season as the Melanosporum.