I think this page sums it up pretty well, in fact giving a general consensus of most of the scholars. According to that, there are no hard and fast rules in determining the exact solar elevation angle. It entirely depends in where you live, i.e. the time when you (in New York) spot the turn over from dark to light might differ when seen from Singapore.
A possible explanation is given that because the sun apparently travels along specific latitude on a specific date between tropic of cancer and tropic of Capricorn, Muslims in various locations around the globe have made observations about Subh-Sadiq and the results are anywhere between 9° to 18°.
And the white thread - black thread is pretty clearly explained as -
Fajr begins at subh saadiq - true dawn or morning twilight when the morning light appears across the full width of the sky. All Islamic scholars agree on this point.
Signs: At pre-dawn, some whiteness appears at the edge of the eastern horizon like a column, this is called (subh kaadhib -false dawn). This whiteness fades after some time and then comes another whiteness (lateral whiteness; second dawn) spreads towards the right and left (full width) through the edge of the eastern sky. This is called subh saadiq (also known as true or second or morning twilight) at this very time the Fajr begins.
I recommend you to go through the section "1. Fajr Dawn-Prayer" of that page, to get a perfect picture.
Based on conflicting estimation, It is our view that, fixing late Fajr time such as 15° could be problematic for those who intended to fast during the day and conversely saying Fajr salaat too early (e.g. 19.5° or 18°) could be equally unsafe.
Therefore 18° is good approximate for sahur (imsak) – extreme limit of pre-dawn meal if one is fasting during the day and 15° is good approximate for start of Fajr. Those prayer tables use 18° for Fajr, it is recommend to wait 10 to 20 minutes before starting Fajr salaat. Equally, complete sahur (imsak) (pre-dawn meal) 10 to 20 minutes Fajr time when using 15° table.
And now finally, to answer your question, no where in the article did the mention of angle less than 9° come up. So, Fajr time is definitely not the civil twilight.
Next, if it is nautical twilight or not. It is pretty difficult to say that. All you can do is simply, follow the trick in bold. To, be more safer,
A thing to note, is according to the rule, both, the start of Fajr Salah time and end of Suhr time are one and the same and above trick is to be just be on the safer side of both.
In the same page, under the section "5. ‘Isha (Night-Prayer)" (I think this is Sunni View), there is a little difference in opinion as to whether Isha start timing is Nautical (12°) or Astro (18°). But, it is better if you consider praying it after Astro twilight except if you're traveling or if you're a Shia, where I think you can pray Isha together with Maghrib i.e. after sunset.
Follow which is in bold above. Or, else, if you know what you're doing, i.e. by following the guidelines under 'Signs:' (see above) and if you're sure, you are able to make out the difference and calculate the apprx. Fajr start timing at your place, then