Nintendo has two forms of revision numbers that they use for their cartridge games. The first one is the "-n" identifier on the end of the serial number which means that something physical about the cartridge has changed. In 99% of the cases this is an update to the label.
Back in the mid-90's we saw a lot of "-1" games appear because common games that everyone wanted to buy were being distributed when the ESRB was being instituted. There are many games that have a standard version and a "-1" revision simply because the ESRB rating was slapped on the label.
Nintendo's own Player's Choice logo is another good example of many label updates that required a new revision number because of the addition of the Player's Choice badge.
What you are really interested in is the ROM version of the game that is on the memory chip on the PCB. For quality control Nintendo does mark their games with a ROM ID on the outside of the game. For any cartridge game with a label on the back (NES, SNES or N64) there is an impressed number on the sticker. For games with only a sticker on the front (GB, GBC, GBA) the number is impressed on the game label, with the exception of the DS and 3DS, which also have the revision stamped on the back.
This number represents the facility/manufacturing line that the cartridge was assembled on. If your cartridge has the first version of the original ROM you will only see the 2-digit facility number. However, if a new version of the ROM was released from the developer to manufacturing, then a letter was appended to the end of the facility code.
The first revision will be an "A", the second revision will be a "B", and so on. If you take a look at these identifiers you can determine which version of the ROM is on your cartridges. If both games have no revision code, or if they have the same revision code, choosing which game to keep is up to you.
The ROM version can be a bigger deal than the serial number variation, depending on the nature of the ROM change. Nintendo has been known to adjust the art in some of their games for no apparent reason. Choosing which revision is a matter of preference.
You may be wondering where to find out information about specific cartridge ROM variations. The best place to go for a detailed log of variations to game ROMs is The Cutting Room Floor. (Beware, this is a blackhole for retro-gamer nerds, such as myself!)
To be clear, this site DOES NOT distribute game ROM files but they have thoroughly documented differences between the software variations of many games, old and new, for Nintendo and many other systems.
The only unfortunate aspect of TCRF is that they do not claim which revision ID stamped on the game goes with which revision detailed on their site. Instead, they just say "Japanese Version 1" or "US Version 2" when outlining differences of ROM versions. You may have to read the details on specific revisions to determine which ones may exist on your cartridges but that's never a difficult process.
The ESRB site lists summaries for the titles they rate. There are differences in the descriptions of the game for each platform (3DS,
DS, PSP,
Windows PC, PlayStation 3, Xbox 360,
Wii); specifically, the 3DS version includes:
Laser sounds, large explosions, and battle cries can be heard during
the sometimes frenetic combat;
while the DS version doesn't.
Best Answer
They are different ROM versions. The first release of the cartridge did not have such a notification. However, the first releases of the cartridge were particularly prone to losing a save file, or even all of the same files.
Nintendo recognized that people may like this battery-powered feature to save games, and didn't want to get a bad reputation of making an unreliable product. So, later releases of the game added that warning, and the instruction manual also contained information to hold the RESET button.
Later, the consensus (from various web forum posts) does seem to be that there were some changes made to how the game was made, making newer cartridges (including electronic copies, like what is found on the Wii) less likely to result in the cartridge losing the saved data. So, later copies of the game took out the message (presumably thinking that the process was less necessary).
Related reading: Arqade: Why is it needed to hold reset when powering off the NES?
According to whicker's forum post on battery saving (which is mostly about the SNES, but also mentions Zelda 1), in a Zelda 1 cartridge, "There's nothing to keep the chip from accepting errant writes." when power levels drop when you turn the system off. Gil_Hamilton's later post (in the same thread) states, "Reading suggests that part of the problem is early games didn't have a capacitor to prevent sudden large voltage changes to the SRAM chip, which aggravated an already-dangerous situation."
The discussions I've seen on this topic seem to be heavier on observations and speculations than solid documentation. The overall impression I got, though, is that newer cartridges did have some design changes.
The Cutting Room Floor: Zelda 1 discusses some changes between different versions of the games. Forum post lists some different versions, like the number of screws that are in the actual cartridge. That may be your best visual difference (other than the color... gold cartridge verses grey cartridge). In summary, there are some differences between the FDS (Japanese version) and the NES version, such as the FDS having more details in the music, and NES Pols' Voice being weak to arrows instead of the FDS microphone. Other differences have been fairly minor, with the most notable differences being the SAVE screen looking quite different, and some text updates. If you're actually likely to notice (I certainly have), your best bet is just to check. Simply by looking at the title screen (including the copyright date), reading the intro text, and visiting the SAVE screen (by pressing Start on the main controller, and then holding A and pressing Up on the second controller) will likely reveal many of the differences that exist, and probably enough to identify which version of the cartridge you have (if you compare your findings to one of the guides that shows comparisons between versions, like some of the resources that I hyperlinked above).