To shed some light on this, both the Trinity CertTESOL and the Cambridge CELTA are offered by a wide variety of accredited course providers. Moderation and assessment are performed by examiners from the respective accrediting bodies (either Trinity College, London or the University of Cambridge), according to a fixed price structure. This price is built into the cost of the course, but the rest of the cost is determined by the course provider. In Hong Kong, it is said that the high cost of rent is the primary reason why the Trinity CertTESOL costs so much (last time I checked, it cost HKD25,000).
In order to gain 'accredited' status, course providers have to fully satisfy the accrediting institutions that they consistently meet all the relevant teaching criteria, and they are regularly visited and have their work inspected to ensure this level is maintained. This is why accreditation is so important. Plenty of on-line or weekend courses will boast that they're 'fully accredited', but unless they're accredited by a reputable establishment after close scrutiny then their accreditations are worthless. You'll see some providers saying they're accredited by the 'World TEFL Council' or some other such nonsense. It then turns out that their accrediting body is owned and run by the course provider's very own college drop-out boss.
This is not to say that Cambridge and Trinity are the ONLY reputable accrediting bodies, but globally they are the most 'recognised'. They are so well-known around the world, and their standards have been consistently high for so long, that employers have great confidence in EFL qualifications coming from either of these two bodies. If you find a course with different accreditation, by all means keep it on the table for consideration, but scrutinise it carefully. Does it come with 100+ hours of 'hands-on' teaching of real students? Does it appear on any Government lists of courses approved for teaching purposes? To what level on the Common European Framework is it equivalent (CELTA and CertTESOL are both equivalent to level 5)?
If you have any reason to doubt the veracity of a provider's claimed accreditation, don't take their word for it. Check directly with the accrediting body.
There is, of course, a whole separate argument about whether one of these two certificates is really needed, especially if you might not be set on making EFL teaching a real 'career' choice, but all that is covered ad nauseum in other threads. You have already got a degree from a UK university and in some cases you'll find that that's enough to get a job. The general consensus on these boards, however, is that either of the top two certificates is a good (if somewhat expensive) qualification to have up your sleeve; having one opens up a lot more 'decent' teaching options (as opposed to teaching in 'fly by night' outfits); and that having a weekend or on-line qualification generally isn't worth the paper its printed on, no matter how cheap the course may be.