Can you explain the difference between textual criticism and higher criticism please?

This text is from a transcript of a talk by David Gooding, entitled ‘Documentary Evidence, Textual Criticism and Translation’ (2007).

Textual criticism used to be referred to as the lower criticism, as distinct from the higher criticism.

The higher criticism was the attempt to date when the documents in the Old Testament and sometimes in the New were written. When it was practised by Wellhausen and Ewald, the presumption was that the order of the Bible that we have at the moment is not original. For instance, Genesis 1:1, 'In the beginning God created the heavens and the earth,' is applying strict monotheism—just one God. People like Wellhausen in the 1800s said that this is impossible because monotheism didn't exist at such an early time, and therefore this is much later, perhaps even after the exile and the return from the exile. So they divided up the Old Testament, according to their sundry principles, into the different sources and the dating of those sources. That was the higher criticism.

Textual criticism doesn't attempt to do any such thing. It is a question of taking the manuscripts and working as best we can from those manuscripts back to the originals.