The link you provided states this:
While the term "subwoofer" technically only refers to the speaker driver, in common parlance, the term often refers to a subwoofer driver mounted in a speaker enclosure (cabinet).
Again: "subwoofer" technically only refers to the speaker driver...
So not true to what you say it seems?
Alternatively known as a sub or woofer, a subwoofer is a speaker that is designed to only reproduce low frequencies, also known as the bass. So Sure, there are speakers that require an enclosure, but that does not necessarily make them 'subwoofers'. Also you can acquire full range speakers and put it in an enclosure not all loud speakers are created to handle 'bass response' as those called subwoofers, subs or woofers.
However that being said, sometimes subwoofers also has been used loosely to suggest a 'loudspeaker' system (which is also has been used loosely to suggest just a subwoofer or a speaker that can produce loud sounds.)
Which can relate to an enclosure that holds a midrange, tweeter and subwoofer.
But again those terms are used interchangeably at times and are not exclusive.
Also when you go to an Audio store or car audio store respectively, Subwoofers usually does not mean an enclosure and amp are included in a Subwoofer sale.
A home audio or computer subwoofer may also refer to the enclosure and an amp. But again that term is used loosely.
Ok so to answer the question of what the 12" Hifonics speakers/woofers/subs/subwoofers require? Depends on the model number. You might check to see if their are any model numbers on the woofers themselves? Otherwise we can only speculate.
As you can see there's a few of them.
What you are really looking for is the RMS and not Peak Power. RMS is the most important. Most of the ones listed in the link from Sonic Electronics state 400-600 watts RMS for one subwoofer.
So if this HFX12D is the exact woofer you have, then what you are looking at is 400 watts RMS for one sub.
The next important step here is the voice coil configuration. You have two woofers, hopefully the same woofer and configuration. What are the voice coils for these subwoofers?
You will need to purchase an amplifier that can handle (if hfx12d is what you have) 800 watts RMS at the specified load for the voice coils and how you plan to have the subwoofers wired.