Fanuc: R636 vs R648 What is difference?

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From your (very) terse description I understand that you are referring to the requirements for the fanuc_driver package, used with Fanuc robot controllers. If that is the case:

• Option R636 (or Socket Messaging) is (as far as I know) the basic package for socket messaging, used by other options on the controller whenever they need to communicate over a network.
• Option R648 (User Socket Msg) is the option that adds the MSG_CONNECT(..), MSG_DISCO(..) and MSG_PING(..) built-ins to the Karel runtime.

Without those built-ins, the ROS-Industrial Fanuc driver cannot function, as it is a Karel application that depends on those routines for its network connections and data transfer.

Can i use R636 package for ROS?

So no, as far as I know, you cannot.

Edit: depending on what other hardware you have, it might be possible to come up with an alternative to socket communication, by e.g. using serial ports. It would limit the driver as the achievable data rates are much lower, but it should be possible. This would require (quite) some development work, on both the Karel sources of the driver as well as the industrial_robot_client side.

The easiest is obviously to buy option R648 from Fanuc and install it on your controller.