My initial assumption is that when someone (e.g. Thatcher) is referred to as a "Low" Tory, it is often a description of a particular type of Tory politics that is fundamentally rooted in an unashamed defense of capitalism and industry and a sort of quasi-anti-elitism (I say quasi, because the notion that the Tories would be genuinely anti-elitist seems unlikely to me - but then again, I'm an outsider to the politics of the UK). My impression is also that "Low" Tories care more about appealing to the morality and culture of the bourgeois and petit-bourgeois middle classes and have fewer ties to the "High" Tory culture of the traditional landed aristocracy and their nostalgic agrarianism.
Finally, I suspect there's a connection between "High Church" Anglicanism (and/or Anglo-Catholicism" and High Toryism on the one hand, and "Low Church" Anglicans (and Protestants in general - Thatcher was a Methodist, IIRC) and Low Toryism, on the other.
From what I understand, this so-called "Low" Toryism was popular among the local levels of the Conservative Party's members and leaders (though I could be mistaken about that...), and it was very popular among affluent middle class Tories. Though this is all, of course, a generalization.
So yeah...am I off base here? Any comments or corrections or further insights would be most welcome!
I think you are overthinking it a little, but you are in the right ball park.
It's quite simple in that Low Torys are pro business and freemarket practice, while High Torys are traditionalists. By very virtue of this your generalisation is fairly true - the Upper class land owning socialites tend to be 'high' and the local middle classes tend to be low (particularly among men). Religion has nothing to do with it, AFAIK.
Assuming you are American (apologies if incorrect) most US conservative viewpoints would sit comfortably as low tory. Low taxation, deregulation of services and industry, privatisation etc.
High Torys are a little bit more English traditionalists. Many are less concerned with economic ideological thinking so long as the UK is a well respected military and economic power with a continuing monarchy.
The terms are less used nowadays as crossover between camps is far more regular, but still exists.
Not sure really how to 'source' this, but a quick google provides this which is a comparison of Thatcher and Enoch Powell among high/low lines which should give a better idea of what it means. Book is Stephen Haslings 'Battle for Britain: Thatcher and the New Liberals'.