I have two budgies. One is the standard yellow head with green body and black markings on feathers. The other is a white with a very faded light yellow/green and grey on the feathers and black eyes. It mostly looks white and grey. I will refer to them as green and white.

Green is very quiet and boring, sits on the perch a lot, doesn't move too much, rarely sings. Will follow white, but not too much activity. Usually stays in the same spot all day

White sings and play. White does acrobatics on the toys, squeezes through the ring toys, squawks loudly, climbs up and down on the cage bars, flys back and forth and green just sits and watches.

Occasionally white will take little cautious steps towards green and suddenly try to bite it. Green watches with beak open and lashes out if white gets to close. White will fly down to a lower perch then come back and do it again. If I put food in the cage, they both sit and look at it, but white is interested and will eventually get closer and closer until it can eat. Once eating, green will participate. I have had these birds since January 09. They must be about 6 months old. I can't tell if they're male or female. Both ceres look the same, a greyish very very slight pink.

Every day since I had them I sit and talk to them throughout the cage. If I put my finger up to the cage they run and huddle to the furthest side of the cage,scared and breathing hard as if a cat is after them. If I put my hand in the cage all hell breaks loose and they fly frantically trying to get away. I have been trying to finger tame them for 4 months now but no luck. I can't get near them at all. Other than that, they are happy and noisy in the cage. I have thought about letting them loose, picking them up with a towel and just talking to them repeatedly. Will this help?

Unfortunately I haven't owned budgies for many many years so I don't remember a great deal about them...

I know that taming takes a lot of perseverance... Make sure you have some yummy treats with you when you come near the birds cage or when you are cleaning it so they associate you with yummy food...

I found this site about how to sex budgies...
Sexing Budgies (helpful guide using 3 of my budgies) - BirdBoard.Com - Parrot Message Board & Pet Bird Owner Forums

Hope that helps a little :)

Good advise above.

You can take them out, one at a time, wrapped in a small towel. Trim their flight feathers. If you are unsure about trimming them, a groomer will show you how. The feathers will grow back. Taming a flighted bird is really difficult.

Then make a small room safe for them. One at a time, take a bird in a towel into the small room. Close the door. Put the bird on your knee - it will flutter away. Gently put it back on your knee, repeat. After about 10 minutes, switch birds. If you do this several times per day they will become used to you.

Until they learn not to be afraid of your hands, always retrieve them from the cage with a towel.

Male Budgies are much more likely to be vocal than females. You can have them DNA sexed for about $20 each.