Short answer
Muslims believe there is only one God, the God of Abraham, Moses and Jesus, and Allah is His name in Arabic. The Quran tells Muslims to say to Jews and Christians, "our God and your God is one" (29:46). But Islam holds that some beliefs about Him, such as the Trinity or God having a son, are wrong.
Sunni creed holds there is one Creator, the One the earlier prophets called to. Hanafi law treats Jews and Christians as People of the Book, which is why their properly slaughtered meat is halal. Yet their belief is not counted as saving faith, because believing in Muhammad ﷺ is part of believing in God's message.
The four schools agree on this.
Explanation
Islam does not see itself as a new religion with a new God. The Quran says to the People of the Book: "We believe in that which has been revealed to us and revealed to you. And our God and your God is one" (29:46). It invites them to "a word that is equitable between us and you: that we will not worship except Allah and not associate anything with Him" (3:64).
So in one sense the answer is yes: Muslims, Jews and Christians all mean the Creator who spoke to Abraham and Moses. Arabic Bibles use the word Allah, and Arab Christians pray to Allah. See Is Allah mentioned in the Bible?
In another sense the descriptions differ, and the Quran is direct about it: "They have certainly disbelieved who say, Allah is the third of three. And there is no god except one God" (5:73). Muslims believe God has no son, no partner and no incarnation. A person can point to the right God and still say false things about Him, and the Quran calls them to correct that.
"Jehovah" is an English rendering of the Hebrew name of God in the Old Testament. Muslims do not use it as a name of Allah, because His names are taken only from the Quran and Sunnah. For more, read People of the Book and Islam and Christianity.
The evidence
Quran, Surah Al-Ankaboot 29:46
۞ وَلَا تُجَٰدِلُوٓا۟ أَهْلَ ٱلْكِتَٰبِ إِلَّا بِٱلَّتِى هِىَ أَحْسَنُ إِلَّا ٱلَّذِينَ ظَلَمُوا۟ مِنْهُمْ ۖ وَقُولُوٓا۟ ءَامَنَّا بِٱلَّذِىٓ أُنزِلَ إِلَيْنَا وَأُنزِلَ إِلَيْكُمْ وَإِلَٰهُنَا وَإِلَٰهُكُمْ وَٰحِدٌۭ وَنَحْنُ لَهُۥ مُسْلِمُونَ ﴿٤٦﴾
And do not argue with the People of the Scripture except in a way that is best, except for those who commit injustice among them, and say, "We believe in that which has been revealed to us and revealed to you. And our God and your God is one; and we are Muslims [in submission] to Him."
Tells Muslims to affirm to the People of the Book that God is one.
Quran, Surah Aal-i-Imraan 3:64
قُلْ يَٰٓأَهْلَ ٱلْكِتَٰبِ تَعَالَوْا۟ إِلَىٰ كَلِمَةٍۢ سَوَآءٍۭ بَيْنَنَا وَبَيْنَكُمْ أَلَّا نَعْبُدَ إِلَّا ٱللَّهَ وَلَا نُشْرِكَ بِهِۦ شَيْـًۭٔا وَلَا يَتَّخِذَ بَعْضُنَا بَعْضًا أَرْبَابًۭا مِّن دُونِ ٱللَّهِ ۚ فَإِن تَوَلَّوْا۟ فَقُولُوا۟ ٱشْهَدُوا۟ بِأَنَّا مُسْلِمُونَ ﴿٦٤﴾
Say, "O People of the Scripture, come to a word that is equitable between us and you - that we will not worship except Allah and not associate anything with Him and not take one another as lords instead of Allah." But if they turn away, then say, "Bear witness that we are Muslims [submitting to Him]."
Invites Jews and Christians to worship the One God alone.
Quran, Surah Al-Maaida 5:73
لَّقَدْ كَفَرَ ٱلَّذِينَ قَالُوٓا۟ إِنَّ ٱللَّهَ ثَالِثُ ثَلَٰثَةٍۢ ۘ وَمَا مِنْ إِلَٰهٍ إِلَّآ إِلَٰهٌۭ وَٰحِدٌۭ ۚ وَإِن لَّمْ يَنتَهُوا۟ عَمَّا يَقُولُونَ لَيَمَسَّنَّ ٱلَّذِينَ كَفَرُوا۟ مِنْهُمْ عَذَابٌ أَلِيمٌ ﴿٧٣﴾
They have certainly disbelieved who say, "Allah is the third of three." And there is no god except one God. And if they do not desist from what they are saying, there will surely afflict the disbelievers among them a painful punishment.
Rejects the Trinity while affirming one God.
Sahih Muslim 153
Sahih... لا يسمع بي أحد من هذه الأمة يهودي ولا نصراني ...
"No one of this nation, Jew or Christian, hears of me and then dies without believing in what I was sent with, except that he will be among the people of the Fire."
Shows that, after hearing the message, belief in the Prophet ﷺ is part of true faith in God.
Where the ruling is recorded
- al-Hidaya, Kitab al-Dhaba'ih, on whose slaughter is lawful. Permits the slaughter of the People of the Book, showing their legal status as followers of a revealed scripture.
- Sharh al-Aqa'id al-Nasafiyya (al-Taftazani), Section on tawhid. Defines the oneness of Allah and rejects any partner or son.
Checked by our team. For a more accurate answer to your own situation, consult a scholar. Quran translation by Sahih International. Hadith Arabic from the standard editions of the six books and the Muwatta, with gradings as recorded there; the English is our own rendering. Spotted a mistake? Tell us.