Platinum Cobra said
Alright I will be the guy that say's something, does anyone else find it weird that you would even ask if it would be a different thing then a basic light saber for a Jedi?
To answer your question, let's look at the facts presented by Star Wars itself.
Jedis who became Sith:
Dooku before he joined the Sith had a Curved-hilt Lightsaber.
Pong Krell before he attepmted to join the Sith used two Double-bladed Lightsabers. Also possibly classified as Lightclubs.
Jedis who became Sith and then became Jedi again:
Bastila Shan used a Double-bladed Lightsaber.
Luke Skywalker used a Shoto Lightsaber.
Jedis:
Jedi Master Kazdan Paratus used a Lightsaber Pike.
Jedi Master Yarael Poof used a Long-handled Lightsaber.
Satele Shan used three different Double-bladed lightsabers over her career.
Jedi Master Tera Sinube used a Sabercane.
Yoda used a Shoto Lightsaber.
Ahsoka Tano used a Shoto Lightsaber.
Ezra Bridger created a Lightsaber-blaster hybrid.
Roblio Darté used a Crossguard Lightsaber.
Maris Brood used a pair of Guard Shoto Lightsabers.
Any more questions?