The comparison doesn't have a great connotation, given that "fundamentalist" is typically an epithet, but it's not too far off in terms of the denotation.

Personally though, I would say it's more of an Exoteric / Esoteric split; conservatives seem to spend most of their effort preserving outward forms and rituals of their cultures in an effort to keep the fire going, where reactionaries see it as burnt out already and so look back for the essential (in both senses of the word) elements to spark a new one. A good example is comparing Chesterton's Catholic apology with Evola's promotion of Tradition, not to imply that you can't be a Catholic reactionary but just as an example of a differing mindset. Of course, esoterica being what it is, it's a bit tough to get a grip on and much easier to talk about than to understand fully.

IANAR, but "fundamentalist" connotes strong deontological beliefs to me, and in particular a stance wherein anything violating some established creed X is definitionally considered evil. That tends to imply at least self-perceived reaction within religious contexts, since most religions' moral contents were developed relative to mores at the times and places of their founding; also because many religions include doctrine describing some sort of lost golden age. But the reverse doesn't seem to be true: we can imagine wanting to rewind parts of society to some prior state on strictly consequentialist grounds, without invoking any particular deontology.

(Indeed, given the amount of variation over time it would be surprising if there weren't historical situations we'd prefer, unless we believe in some sort of ethical teleology or an Yvain-style deal where the ethical sophistication we can get away with supporting scales with technical capability, at least in agrarian/industrial societies. I find the latter somewhat convincing, myself.)