Can you hold finches, or will they fly away and be frightened, also can you hold budgies or are they the same?

Most finches won't perch on your finger or become tame. They don't like to be held. They are very shy, skittish birds that would rather fly around their cage, sing, and enjoy another finch's company. Some budgies enjoy perching on your finger or sitting on your shoulder. It's a good idea to get a budgie that has been hand-fed and is already socialized if you want a friendly budgie. Many store bought budgies haven't been socialized and it can take many months to tame them.