Is Allah the same God that Christians and Jews worship?

۞ 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 argue not with the People of the Scripture unless it be in (a way) that is better, save with such of them as do wrong; and say: We believe in that which hath been revealed unto us and revealed unto you; our Allah and your Allah is One, and unto Him we surrender.

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 an agreement between us and you: that we shall worship none but Allah, and that we shall ascribe no partner unto Him, and that none of us shall take others for lords beside Allah. And if they turn away, then say: Bear witness that we are they who have surrendered (unto Him).