|Martian Manhunter THROOMs General Zod, and then gets THWAMmed in return, in this page from Superman/Wonder Woman #3 drawn by Tony S. Daniel and Matt Banning|
The latter is just what it sounds like—blasts of intense heat that blast out of Superman's super-eyeballs in a concentrated ray, usually drawn as a visible red eye-beam (Comics being a visual medium and all). But it was my understanding that the former was some form of laser beam or concussive blast, rather than simply heat-vision under a more local name (Examples of the pair of them shooting their eye-beams in the same panel are relatively rare, but I do recall it happening at least once during the Morrison/Porter/Dell JLA run, and in that case J'onn's martian vision beams were colored darker than Superman's heat-vision, more purple than red.
In Superman/Wonder Woman #3, however, it seems like J'onn's martian vision is basically heat-vision, of a sort.
Seeking to capture a mysterious and powerful visitor from a different dimension (General Zod, actually), the Justice League of America's Steve Trevor has Vibe use his, um, vibrational powers to kick up a cloud of sand around Zod, and then says the following to J'onn:
Just how vulnerable J'onn is to fire, and the whys and wherefores of it, have changed over the years, of course. Pre-reboot, it was more of a psychological fear than a physical weakness, more debilitating phobia (like Storm's claustrophobia) than Achilles' heel (like Superman's kryptonite), although during his JLA run Joe Kelly played with it in a way to suggest that it's a psychological block meant to keep a monster of the Martian collective unconsciousness at bay.
After the New 52-boot, I don't know J'onn's status in regards to fire (His history is a bit confused, to say the least, at this point, most of it having occurred off-panel, in the undocumented five missing years), but if he's afraid of or somehow vulnerable to his own eye-beams now, well, that's a pretty big change.
To answer the question suggested in the title of this post, however, I would assume that Soule is right and that I'm wrong, given the fact that he's a professional writer hired by DC Comics and is writing comics edited by editors at DC Comics, while I'm a guy who reads DC comics and then complains about their shortcomings (if any) on the Internet.
And perhaps the New 52 continuity reboot changed the very nature of J'onn's Martian Vision...?
Except that would be really weird if they actually sat down to redesign and reimagine J'onn J'onnz and were like, "Okay, let's streamline this character to make him more accessible to more readers. We changed the shape of his head, added a loin cloth over his pants, put him on StormWatch instead of the Justice League...what else? Oh! Let's alter the nature of his eye-beams, so now they are even more like Superman's, and also he doesn't like using them, because he doesn't like heat, because heat comes from fire."