Are both correct ?
When writing an official form+document, which one should I use?
It depends. If you apply to a computer services company (Fr : Entreprise de Services Numériques (ESN) , formerly Société de Services en Ingénierie Informatique (SSII)), a generic label is
Ingénieur Etudes & Développement.
However, keep in mind that we are talking about a "generic label" and not an official title.
The only title you will be able to find in France is
Engineering schools get their accreditation from the CTI (Commission des Titres d'Ingénieur). If you have this title, use it. Otherwise, I recommend
Ingénieur en Informatique for the reason below if you want to stay generic.
Are there any difference between those two?
Litteraly speaking, no. Except they suggest a different personality.
Ingénieur informaticien is a bit 80s so you would prefer the other one.
Any french software engineer eventually hears about this video : Michel l'ingénieur informaticien sur YouTube. There are other humorists (Les Inconnus, for instance) that made fun of nerdy software guys at that time, so you normally want to avoid that label :)
I personally don't like new titles as "Ingénieur NTIC, Ingénieur IT, etc" as you don't know what it means (network ? software ? admin ? coffee ?).
When specicifying "Ingénieur" in your resume, you suppose that you have a Master degree in computer science. (Traditional engineering schools last 5 years in France).
I prefer to specify the area I mainly work on. I use "Ingénieur en Développement", as I work as a developer and have a master degree (and the title /bling /bling). You can use "Ingénieur X" according to your activity.