Okey doke.
Looks like you could use some clarification about several things here. Hopefully, I'll be able to help
First up, that's a nice, vintage Denon receiver you've got there! Really good amplifiers they had back then. So you've got a nice start
It's called an "A/V Receiver" - the "A/V" stands for "Audio/Video"
There IS such a thing as a "passive" subwoofer, which is a subwoofer that draws its power from the A/V Receiver. But the Sony subwoofers that you are looking at are "powered" subwoofers. Powered subwoofers are far more common than "passive" subwoofers - at least for consumers.
A powered subwoofer has its own amplifier built-in. A powered subwoofer has its own plug that you plug into the wall. When you are looking at the specifications for those Sony subwoofers, they are saying how much power the amplifier that is built into the subwoofer can generate. So you do not have to worry at all about whether or not your Denon receiver can power the subwoofer. The subwoofer will be using its own plug and making its own power.
The "120V - 60Hz" specification refers to the type of plug that the subwoofer or receiver uses. "120V" stands for 120 Volts. And 60Hz stands for 60 Hertz. "120V - 60Hz" power is the standard power outlet in North America. Almost every plug in your home (if you live in North America) is a 120 Volt 60Hz plug. Exceptions would the the large plugs for your clothes dryer and your electric stove. Those are higher power plugs that use 240 Volts.
So, all you really need to know is that both your Denon receiver and those powered subwoofers are meant to plug into any standard power receptacle in North America
Now, let's talk a little bit about your Denon receiver and how you will connect a subwoofer to it.
That DRA-835R receiver does not have any dedicated "subwoofer out" plug. It is a straight-up Stereo receiver. A 2.0 receiver, not a 2.1 receiver. Most subwoofers these days are designed to be used with a dedicated "subwoofer out" connection. Both of those Sony subwoofers are meant to be connected to a single "subwoofer out" connection.
Now, your Denon receiver DOES have a pair of left/right "pre out" plugs. What you can do is simply connect the subwoofer to just the "left" pre out plug and leave the "right" pre out plug without any connection.
There might be some very rare cases where you won't get all of the bass in the recording if you connect your subwoofer this way. For example, if the bass in the recording is only coming from the "right" speaker for some reason, then the subwoofer won't play it if it is only connected to the "left" pre out as I have just described.
You could use a "Y-plug" cable to connect both the left and right "pre out" plugs to the single "line in" plug on the back of the subwoofer. But this can cause some problems. If you "funnel" both the left and right "pre out" plugs into a single plug for the subwoofer, then when the bass is coming from both speakers (which is most of the time), the signal will essentially be "twice as loud" as it really ought to be. On the other hand, when the bass is only coming from the left side or the right side, but not both (which is rare, but it can happen sometimes), then the subwoofer might sound too quiet because you will have adjusted it so that it sounds correct when the bass is coming from both speakers.
So there is a third connection option - but you will have to look carefully for a subwoofer that will allow this type of connection. Some subwoofers have speaker terminals on the back. You can run speaker wire from the speaker terminals on the back of your Denon receiver to the subwoofer and then run speaker wire from the subwoofer to your speakers. This is probably your best option, but you have to look for a subwoofer that has speaker terminals on the back to allow for this connection.
A final, fourth option - there are some subwoofers that have a left and right input plug. This would be the ideal option for you. You would simply connect the left and right "pre out" plugs on the back of your Denon to the left and right input plugs on the back of the subwoofer. This connection type is rare these days though, so you would have to look very carefully to find this option.
In this very low price range for subwoofers (under $150), there are not a lot of good options. Personally, I do not think the Sony subwoofers are very good. Personally, I would rather see you save up some more money so that you could buy a much better subwoofer. For example, for $300, the HSU STF-1 would be a good option, and it has those speaker terminals that I mentioned, so you could run speaker wire from your Denon to the HSU subwoofer and then run speaker wire from the HSU subwoofer to your speakers.
In the $150 price range, I quite like the Onkyo SKW-204 subwoofer, but it only has the single "line in" input that is meant to be used with a "subwoofer out" plug - just like the Sony subwoofers. So it does not have an ideal connection option, but it is a pretty good little subwoofer for the very low price.
Perhaps your best bet though would be the $250 M8 subwoofer from Outlaw Audio. It is small, it is substantially better than the Sony subwoofers or the Onkyo subwoofer. But best of all, it has the "ideal" connection option of left and right input plugs to perfectly match the left/right "pre out" plugs of your Denon receiver. It also has speaker terminals if you prefer to use speaker wire like you would with the more expensive HSU STF-1. The M8 is $100 more than you were looking to spend, but I personally think you would be very well served and happier in the long run if you saved up that extra $100.
Finally, I am almost certain that someone will recommend a Dayton subwoofer to you. You can find them at parts-express.com and the Dayton SUB-100HT would be the one that fits your $140 target price tag. It's tough to complain about the Dayton subwoofers because they are so inexpensive. What people like most about them is that they play quite loud for their size and especially for their price. So people like them for movies where they are more worried about just creating loud rumbles and explosions. But personally, I just find that the inexpensive Dayton subs produce too much distortion and aren't very accurate for music. I actually prefer the Onkyo SKW-204 subwoofer for about the same price in terms of sound quality. However, the Dayton SUB-100HT has that "ideal" connection option of left and right input plugs as well as speaker wire terminals. So, if you really, really need to stick to that $140 price tag and cannot save up for the Outlaw Audio M8 or the HSU STF-1, then the Dayton SUB-100HT becomes probably your best option. It is at exactly the price that you want. It has the "perfect" connection options. And most people who buy it are really happy with it because it plays loud and it can "hit you in the chest" for explosions and rumbles and such. It honestly isn't my first choice in terms of pure sound quality for music, but that is only my personal taste and there are certainly a lot of other people who are really happy with the Dayton.
So, I think that should give you pretty much all of the info that you need! I do not think that you should buy the Sony subwoofer. It isn't very good and it doesn't have the best connection options for your Denon receiver.
Hope this helps!
