Is there a difference of movement between VF4 and VF5:FS?

Not exactly sure what your friends are referring to, especially with the "move and attack simultaneously" part. If it's referring to attacks that comprise of a dash input (e.g. ) then that hasn't really changed at all.

Perhaps they're referring to the ability to attack while evading (another type of movement)? VF4 had special "evade attacks" which were completely removed in VF5.

Perhaps they're referring to the ability to cancel one type of movement with another? This changed between VF4 and 5. In VF4 you could only cancel a failed evade with a forward crouch dash, but in VF5 you can cancel it with standing dashes, so in that regard evade cancels were made "easier" in VF5.