Here is my rundown of the 6JC5/6JB5/6HE5 family of tubes as I presently know it.
(this is from some testing/using/examining plus net searching)..
The 6HE5 is the small bottle version with the small 12w plate.
(all the brands seem to make these, slightly smaller bottle then a 7868)
http://www.mif.pg.gda.pl/homepages/frank/sheets/123/6/6HE5.pdf
The 6JB5 is the larger bottle version and an larger 15w plate.
(these seem to all be GE, but re-branded as well)
http://www.mif.pg.gda.pl/homepages/frank/sheets/123/6/6JB5.pdf
The 6JC5 is also larger bottle version with a larger 19w plate.
(these seem to all be Sylvania, but re-branded as well)
http://www.mif.pg.gda.pl/homepages/frank/sheets/107/6/6JC5.pdf
Then there is the RCA 6HE5/6JB5, large bottle with small 12w plate.
(these seem to have the small 12w 6HE5 guts in that larger bottle)
I have ran them all, the Sylvania seem the beefiest an sound best, (to me at least)
(in Singled Ended UL I get 5-6w output, push pull pentode here you'd be say 23w)
The 6JA5 has the same pinout, but is not exactly the same tube an draw more PL
current to where they do not bias up anywhere near where the others do.
(I believe these are a 19w rated plate as well)
The tubes labeled with all 3, 6JC5/6JB5/6HE5 on them should be your large bottle
GE and Sylvania tubes, I would search those out..
Now to get funky, there is another set of tubes with a top cap plate connection an
with 17.5/18w plates, 6GV5/6GY5, if you look at the pinouts, you can see they can
be wired to use the same pinout/socket as the above just need the plate caps con.
(I have not used these so I don't know how they respond)
http://www.mif.pg.gda.pl/homepages/frank/sheets/123/6/6GY5.pdf
(I wouldn't pay more then $5 ea for these tubes, plenty out there for that price)

A couple places I have bought tubes from with good service and prices are here.
http://www.fourwater.com/compact/comp_c5.htm
http://www.esrcvacuumtubes.com/vacuumtubes_tubelist_tubes_5A5-5Z4G.html
======== These have also been referred to as 6V6's on steroids (not by me)
My camera isn't the best but here is a bit of comparison of how these tubes look
next to each other. (should give a decent example of there physical differences)
First pic shows left to right, 6HE5, GE 6JB5, Sylvania 6JC5
Second pic shows left to right, 6HE5, RCA 6HE5/6JB5
Third pic shows left to right, RCA 6HE5/6JB5, Sylvania 6JC5
Fourth pic shows left to right, GE 6JB5, Sylvania 6JC5
== (the Sylvania has a distinctive rectangular internal structure)