Maybe its me, but the term semi pro seems misleading. Small publishers vs corporate publishers are both pro markets...
To me, I would never say my doctor is a semi pro, and I really don't go to semi pro lawyer. That would be dangerous...
I don't think that analogy really holds up, mostly because to be a doctor or a lawyer, you have to pass a whole bunch of exams first, and really any noob with a website can declare themselves a publisher (and potentially make good of it.)
That aside, there are two functionally useful applications of those descriptions:
1) As set by SFWA based on a combo of criteria like pay rate and circulation. (I have no idea if BSFA uses/follows the same classifications, but if someone knows and wants to enlighten, I'd love to hear.) Some mags right on the edge, like Interzone, are considered pro by just about everybody but don't quite make the cut on figures for that rating, which is why it usually shows up in the Hugo "Best Semi-Prozine" category, but gets listed along with the pros in Locus' annual breakdown of the state of the industry.
2) As a simple measure of pay-rate to the author. I've seen markets listed as paying semi-pro where, by dog, I could put together something better in my spare time even while drunk, blind-folded, and trying to type with boxing gloves on, and I've seen markets paying much less that are just absolutely wonderful as both a writer AND a reader.
As an author, you should know what any mag pays (and buys for rights, because not all will actually cough up a contract) before you sub a story to them, and have at least some idea what the prestige-level of the mag is, because you want to get paid and you want lots of people to read your stuff. (For me, with it's the latter that I care about more, but that may not be true for everybody.) Not that those are the only considerations you should have before sending your work off -- frex, I've subbed to underpaying markets where I liked their concept and wanted to be a part of it -- but it gives you a place to start and a sense of how a market is regarded by the writing world at large.