In practice, there is no difference between not copying the card and not playing the copy, because there are no cards or interactions that care about either. In theory, "game state" is an official, yet ill-defined term and at the moment, there is no correct rules-based answer whether or not the different options could have different effects on the game state.
A copy of a card is created in the same zone the original is in:
706.12. An effect that instructs a player to cast a copy of an object (and not just copy a spell) follows the rules for casting spells, except that the copy is created in the same zone the object is in and then cast while another spell or ability is resolving. Casting a copy of an object follows steps 601.2a–h of rule 601, “Casting Spells,” and then the copy becomes cast. Once cast, the copy is a spell on the stack, and just like any other spell it can resolve or be countered.
If you choose to copy a card but don't cast it, it ceases to exist as a state-based action the next time a player would get priority:
704.5e If a copy of a spell is in a zone other than the stack, it ceases to exist. If a copy of a card is in any zone other than the stack or the battlefield, it ceases to exist.
Since to my knowledge there are no effects that care about a copy of a card, or any object for that matter, ceasing to exist, there is no practical difference between not copying a card and not casting the copy.
As for effects on game state: The term is used loosely in the CR. It is used 16 times throughout the current rules, but is never clearly defined - it doesn't even have an entry in the glossary, even though state-based triggers depend on it:
603.8. Some triggered abilities trigger when a game state (such as a player controlling no permanents of a particular card type) is true, rather than triggering when an event occurs. These abilities trigger as soon as the game state matches the condition. [..]
The shortcut rules come closest to defining game state as "anything that happens in the game that some ability or effect might care about", which isn't all too helpful, because the definition is essentially circular: the game state determines what the game state is.
720.3. Sometimes a loop can be fragmented, meaning that each player involved in the loop performs an independent action that results in the same game state being reached multiple times. [..]
Example: In a two-player game, the active player controls a creature with the ability “{0}: [This creature] gains flying,” the nonactive player controls a permanent with the ability “{0}: Target creature loses flying,” and nothing in the game cares how many times an ability has been activated. Say the active player activates his creature’s ability, it resolves, then the nonactive player activates her permanent’s ability targeting that creature, and it resolves. This returns the game to a game state it was at before. [..]
In the loop example, activating the two abilities once each is game state neutral. However, if something else was in the game that cared about the activations, the activations would not be neutral. Especially in a game with hidden information, having an ill-defined game state is unfortunate, to say the least.
The point is, going by the example of 720.3, creating a copy of a card and not casting it is the same as not creating a copy of a card, because nothing cares about either of the two options. But there is no rules reference to say for sure either way.
As for your wording: I do not find it equivalent to the current wording. I take it you mean to say that
You may (copy the exiled card and cast the copy without paying its mana cost.)
However, a player could also understand
(You may copy the exiled card) and (cast the copy without paying its mana cost.)
There is potential for confusion, since a player could rightly ask how to cast the copy if I declined to create it? The current wording leaves no room for interpretation and reduces player confusion, which is good design outside of the mechanical details.
As for rules interactions, combining the two instructions of copying and playing the card is equivalent to the current wording of two separate decisions. However, if anything in the future ever cared about copying cards and/or letting them cease to exist by not casting them, all cards with your proposed wording would require errata, or rather, could have unintended interactions such as being required to cast a spell just in order to get a copy first, if all you want is a copy.
