Qur’an states that on the Day of Judgment the pregnant women will abort. Is this similar to what people do nowadays?

What you are speaking about is mentioned in Surah Al Hajj Verse 2

يأَيُّهَا النَّاسُ اتَّقُواْ رَبَّكُمْ إِنَّ زَلْزَلَةَ السَّاعَةِ شَىْءٌ عَظِيمٌ - يَوْمَ تَرَوْنَهَا تَذْهَلُ كُلُّ مُرْضِعَةٍ عَمَّآ أَرْضَعَتْ وَتَضَعُ كُلُّ ذَاتِ حَمْلٍ حَمْلَهَا وَتَرَى النَّاسَ سُكَـرَى وَمَا هُم بِسُكَـرَى وَلَـكِنَّ عَذَابَ اللَّهِ شَدِيدٌ

(O mankind! Have Taqwa of your Lord! Verily, the earthquake of the Hour is a terrible thing. The Day you shall see it, every nursing mother will forget her nursling and every pregnant one will drop her load, and you shall see mankind as in a drunken state, yet they will not be drunken, but Allah's torment is severe.)

So, that abortion will be natural abortion where the child will come down prior to its term, and not the abortion done by people today.