Is there a difference between subh prayer and fajr prayer?

Fajr prayer
is subh prayer – there is no difference between them. It consists of two
rak’ahs. The time for this prayer starts when the true dawn begins, and
lasts until the sun rises. There is a prayer that comes before it,
consisting of two rak’ahs, which is known as the Sunnah of subh or the two
rak’ahs of Fajr. 

The phrases
salaat al-subh and salaat al-fajr are both used in the Sunnah
to refer to this prayer, such as the report narrated by Muslim (656) from
‘Abd al-Rahmaan ibn Abi ‘Amrah who said: ‘Uthmaan ibn ‘Affaan entered the
mosque after Maghrib prayer and sat by himself. I sat beside him and he
said: O son of my brother, I heard the Messenger of Allaah (peace and
blessings of Allaah be upon him) say: “Whoever prays ‘Isha’ in congregation,
it is as if he spent half the night in prayer, and whoever prays Subh (Fajr)
in congregation, it is as if he spent the entire night in prayer.” 

Al-Bukhaari
(556) and Muslim (608) narrated that Abu Hurayrah (may Allaah be pleased
with him) said: The Messenger of Allaah (peace and blessings of Allaah
be upon him) said: “If one of you catches up with a rak’ah of ‘Asr prayer
before the sun sets, let him complete his prayer, and if he catches up with
a rak’ah of Subh (Fajr) prayer before the sun rises, let him complete his
prayer.” 

As for
calling it Fajr prayer, Muslim (670) narrated from Jaabir ibn Samurah that
when the Prophet (peace and blessings of Allaah be upon him) prayed
Fajr he would sit in the place where he had prayed until the sun was well
risen. 

And
al-Bukhaari (891) and Muslim (880) narrated that Abu Hurayrah (may Allaah be
pleased with him) said: The Prophet (peace and blessings of Allaah be
upon him) used to recite in Jumu’ah and in Fajr prayer, “Alif‑Laam‑Meem.
The revelation of the Book… ” [Soorat al-Sajdah, no. 32] and “Has
there not been over man a period of time” [Soorat al-Dahr, no. 76].  

And
al-Bukhaari (555) and Muslim (632) narrated from Abu Hurayrah (may Allaah be
pleased with him) that the Messenger of Allaah (peace and blessings of
Allaah be upon him) said: “Angels come to you in succession by night and by
day, and they meet at Fajr prayer and at ‘Asr prayer, then those who stayed
among you ascend and He (Allaah) asks them, although He knows best, ‘How did
you leave My slaves?’ They say: ‘We left them when they were praying and we
came to them when they were praying.’” 

See also
question no. 65941 and
26763 for information on the time of Fajr (Subh)
prayer, and question no. 65746 for more information on the Sunnah of Fajr
prayer. 

And Allaah
knows best.