Red wire vs green wire

[RubusRoo]

what is the differnce between them or are they just required for different recipes?

[KatherineOfSky]

They are used to create circuit networks, and keep values separate. There is no functional difference.

[Qlimax]

Red wires look nicer and green wires can blend in with grass better for that conceiled look

[Phoenix]

One is red coloured.
The other is green coloured.
Hope this helped.

[Jupiter3927]

As Katherine said, They do the exact same thing but won't add values together if they're on the same power pole like similar colored wires.

Useful for running a big circuit network across a small network without letting them interfere with eachother.

[BitterSwede]

If you are familiar with radios at all, or radio-like apparatuses, like WiFi, you can see them as 2 different channels. They can transfer different information at the same time.

Say you have a chest and you want an inserter to know how much iron ore is in the chest and an alarm to know how much iron ore is in all chests minus that one. You could set up an arithmetic combinator on the red channel, taking the amount of ore in all chests and a green wire taking the amount of ore in that one chest. Now you can run the green wire to the inserter directly, and a wire of any colour from the combinator to the alarm.
The green wire will not show what's in all chests, just that one chest, while the red wire will not show what's in that one chest, but all other chests, despite both wires being connected to the same machines and poles.

A bit of a rubbish example, people tend to do more useful stuff with it, like running them along train tracks having green for the loading information and red for the unloading information, but I hope that example shows how the wires work on the most basic level.