What separates the OPL from the OPL2 is the OPL can only use sine operators like the OPM and OPN chips (but again, only 2-op, instead of 4.) What the OPL2 (and the rest of the OPL line, including OPLL) added to the mix is the ability to use operators that were not plain sine waves. This doesn't go so far as to completely offset the disadvantage of only being 2-op...definitely not...but it does go part of the way by making up for sounds it can't do that the others can with sounds it can do that the others can't (so, perhaps you could say that where OPM and OPN are deep, OPL2 is wide).
OPL2 could use for its operators either plain sine, half sine (with the bottom - negative half of the waveform gone, replaced with flat space), absolute sine (with the negative half inverted, leaving two positive halves), and quarter sine (the negative half gone, the positive half half gone, leaving something almost resembling a rounder, more staccato sawtooth wave).
While OPL2 was more prominent in PC gaming (via the Ad-Lib, and early Sound Blaster cards) than it was in the Arcade, and while just about every appearance of the OPL2 in the arcade (of which there were many) saw it paired with a YM2203 (OPN) or doubled up (as were the case with Truxton, and Midnight Resistance, etc), there were a few Arcade games that used just a single OPL2 exclusively.
When compared to an OPN or OPM soundtrack, this chip does still sound pretty "vanilla FM"...but when compared to the YM3526 OPL, this sounds positively diverse, and spacious, and...just so much better. OPL2 was a dramatic upgrade over OPL, even though the basic skeleton underneath remains the same.
Here's a video to the OUT ZONE Arcade soundtrack that uses an OPL2 for its soundtrack. The video opens with an arranged version of something. That's not OPL2, of course. But if you either skip that track, or wait it out, everything that follows is OPL2.
Another game I found that uses just an OPL2 is Demon's World (aka Horror Story). I couldn't find a video that features a full soundtrack. But here are a handful of tracks from the game.
Now here's an example of a PC game using the chip (on an Ad-Lib sound card) - Dune II
Now, these are examples of games that just use a single OPL2 chip. In PCs, that was pretty common for a certain era. However, for the Arcade, a single OPL2 chip was actually pretty rare. OPL2 showed up a lot, but usually paired with something. The following two soundtracks, Midnight Resistance, and Truxton each use two OPL2 chips running in tandem, hoping the bury the limitations of the chip in an absolute deluge of channels, I suppose...I'd say it sorta kinda works.
Midnight Resistance goes even further, not only using two OPL2 chips, but also using a PCM sampler for percussion.
But when you compare this 22 channel sound frankenstein with the Sega Genesis' [by comparison] meager 10 channel setup of the YM2612 (OPN2) / SN76489 (four channels of which are just PSG), you can still very clearly see the limitations of 2-op FM compared to 4-op, even with four available operator waveforms vs just one (and this is even with the Genesis version not using sampled percussion, just FM). Here's the Genesis version of the same soundtrack
But even more common than seeing a "stacked double OPL2" scheme, was seeing the OPL2 paired with an OPN (YM2203). It's really a brilliant set up, to be honest. The OPN only has three FM channels, and they're sine-only operators - BUT, they're 4-op channels, so you have three channels of deep complex FM, paired with the OPL2, which is only 2-op, but four available waveforms and a whopping nine-to-eleven channels! So, the idea is you use the OPL2 for the nuts and bolts of your music, with the OPN for the highlights. Here's a soundtrack that exemplifies this OPL2/OPN approach - The Sly Spy!
And I'll leave you with one more Arcade game to use the OPL2/OPN duet setup - Bad Dudes!