I think this makes the distinction
https://www.google.fr/url?q=https://www.vocationaltraininghq...

--------------------------------------------------
Note added at 23 hrs (2018-06-23 07:36:11 GMT)
--------------------------------------------------

I imagined vocational as work-oriented, along the lines of an apprenticeship here (whose definition includes study). An apprenticeship is a Formation', do you think it might fit better?

https://en.wikipedia.org/wiki/Professional_qualifications_in...

I would normally suggested for 'diplômant" - "leading to a diploma/qualification". Here I have turned things around a little to make it less cumbersome as there are two elements.
training = formation ; leading to = "-ant'; etc.

--------------------------------------------------
Note added at 1 day 5 hrs (2018-06-23 13:35:11 GMT)
--------------------------------------------------

I am going to have another stab at this:
training leading to a (state) recgnised diploma / professional development training.
This seems to conform to the idea that it will allow the employee to improve his/her skills, maybe be eligible for promotion, but within a field or firm
https://www.glassdoor.com/employers/blog/5-ways-to-encourage...
https://research.utwente.nl/en/publications/promoting-teache...

"La Formation diplômante donne un diplôme reconnu par l’Etat (CAP, Bac, BTS, etc.)" :
This course/training provides the successful person with a diploma that is recognised by the State.
The difficulty is that a CAP, a Bac Pro and a BTS are also vocational within the English meaning of the term.

"La Formation qualifiante (CQP, DQP, etc.) donne un certificat qui peut être reconnu par des branches professionnelles mais pas par l’Etat."
This course/training provides the successful participant with a diploma that has a professional application.
Note that the FR says "may" be recognised by one (prof) but not the other (State). It does not say that the State does not ever recognise such diplomas.

Example : My Masters 1 in Psychology from a French university is a qualification (UK meaning) that is recognised by the State. It does not give me any recognised vocational qualification at all. However, if I complete an M2 in Psychology (in any field except in Business Organisations), I can obtain the professional qualification as a psychologist and will be able to exercise as such in France.
I also have a DU in Autism, but it is just a diploma, conferring no vocational rights or title. It is described as a "formation diplomante" conferring no professional rights or title.

These terms are awkward to express and I think the definition of the second (qualifiante) is a little confusing. Note that it does say "qui peut être reconnu par des branches professionnelles mais pas par l'Etat". It says "may be recognised by a professional branch but not by the State"; some are recognised by both. An M2 in Clinical psychology is both recognised by professional bodies within France and by the State. I think this should not be overlooked as if you are not careful here, you can easily give the impression that the "diplomante" is state-recognised and that the "qualifiante" is never state-recognised, whereas the latter can be.

Between them, Ormiston and Katsy's answers seem to have it pretty well sewn up. I'm only posting to illustrate my experience and understanding. Not easy to tra,slate into (UK) English though, as "qualification" is often the best way to translate "diploma". To avoid misunderstanding and to avoid the client thinking that the two terms have been confused, there is need for a bit of a trade-off here.

Also, in context, each term is defined, so that can be taken into account in the rendering here. Indeed, the definitions save the day. I prefer to use "professional" in the second instance as some State diplomas are vocational.
Different conceptions and tricky to translate.

--------------------------------------------------
Note added at 2 days 12 hrs (2018-06-24 20:26:09 GMT)
--------------------------------------------------

Even "certifying" is awkward, as I intend it to mean that you get a certificate, not that it necessarily certifies you to occupy a particular professional role.