Legendaries represent a unique character, other cards represent a spell or a class/title. This is also why you can only have one of each legendary in your deck, but two of each of the rest of the cards.

There's only one Lord Jaraxxus and one Lorewalker Cho, their names are unique. The other cards have general names only describing them and/or their job, Bloodfen Raptor, Armorsmith and Angry Chicken for example.

Single Turn

It is possible to get 14 Thaddius' on the board, 7 for each player. There are many ways to do this, but here is a possible scenario:

Mage vs. Priest

1. Priest plays Mind Vision twice, getting 2 Stalaggs.
2. Priest plays Thoughtsteal, getting 1 more Stalagg.
3. Priest draws his or her own Stalagg and Feugen and plays Feugen.
4. Mage plays Stalagg and Duplicate.
5. Mage draws Feugen.
6. Mage attacks Priest's Feugen with his or her Stalagg, producing two Thaddius' and duplicating the Mage's Stalagg.
7. At this point, both players have one Thaddius each, the Mage has three Stalagg/Fuegen's in hand and the Priest has four Stalagg/Fuegen's in hand.
8. Mage plays his or her three Stalagg/Fuegens.
9. Priest plays his or her four Stalagg/Fuegens.
10. Mage plays a Duplicate.
11. Both players kill eachother's Stalagg/Fuegens causing the Mage to get two more.
12. Mage plays his or her two remaining Stalagg/Fuegens and they die.
13. At this point, Mage has six Thaddius' and Priest has five Thaddius'.
14. Mage plays a Faceless Manipulator to complete his or her seven Thaddius set.
15. Priest plays two Faceless Manipulators to complete his or her seven Thaddius set.

Multiple Turns

A very large number of Thaddius' can be produced over an entire game, too many for me to count. Here is why:

Priest vs. Priest

1. Each Priest draws a Thoughtsteal. One draws Stallag and one draws Feugen.
2. Each Priest player has a Stalagg/Feugen and a Thoughsteal as the bottom two cards of their deck.
3. Starting on turn 2 for the 2nd Priest player, each Priest player plays a Thoughtsteal every turn.
4. Every Thoughtsteal through an amazing random number generator miracle gets the bottom two cards of the opponent's deck (a Stalagg/Feugen and a replacement Thoughsteal).
5. Starting on turn 8, the Priest players start playing both a Thoughtsteal and a Stalagg or Feugen.
6. Both Priests trade Feugen and Stallagg producing Thaddius, which they then trade.

Therefore, starting on turn 9, two Thaddius' are produced every turn until one of the Priest players dies from Fatigue (which Priests can survive for a while).