Udhay Titus has made a couple of important questions about an (according someone) alleged discrepancy of the Hebrew Bible.
The questions are:
(1) What is the difference between of these two verses (Gen 1:24 and 2:19)?
Or, (2) what is the exact meaning of these two verses?
To respond to the first question, we are able to say that the difference between of these two verses is the purpose, or aim of the point of the passages.
In the first instance - Gen 1:24 - the writer’s aim is to describe – synthetically – how land animals appeared for the first time on the planet Earth, being this verse – with full rights – inside the ‘Creation Spans of Time’ (or, popularly called, ‘Creation Days’), and more exactly, the Sixth of them.
In the second instance (Gen 2:19), its writing purpose is totally different. We may conclude so by the context itself. In fact, the logical paragraph (verses 18-24) points to the God’s necessity to provide a mate to man, as all the animals have yet.
The verse 18 tells us: “And Jehovah Elohim said, ‘It is not good that Man should be alone; I will make him a helpmate, his like’.” (Darby)
Here, Jehovah Elohim is described like a man who contemplate a produced masterpiece of him, trying to evaluate if it is possible to improve – in some way - the artifact.
Logically, this wording must be viewed as a kind of anthropomorphic device. In fact, the (outer and inner) structure of man’s body itself – based on the God’s choice to make possible the multiplication of humans through a sexual method (a number of God’s matter creatures don’t use this method. In fact, they use some asexual reproduction methods, as fission, budding, fragmentation, or parthenogenesis) - clearly pointed to some necessary mate, in the same moment of his devising (in the mind of God)! We have to remember that all the creations of the Almighty were – before the real creation of them – imagined, or devised in the mind of God. We find a beautiful wording of this process in Rev 4:11 (bold is mine):
“Worthy are you, our Lord and God, to receive glory and honor and power, for you created all things, and by your will they existed and were created” (ESV).
They (“all things”) ‘existed’ before in God’s mind, intentions, ideas, thoughts; and after, they were ‘created’.
In the second part of the verse 19 and throughout the verse 20, we see – first – the God’s assignment to Adam to nominate (“literary to designate or specify […] by name” [The Penguin English Dictionary, 2nd Edition]) all the animals, and afterwards, how Adam performed this assignment, diligently.
But, note – now – the key-words of the entire topic (Gen 2:20):
“[…] but as for Adam, he found no helpmate, his like.” (Darby)
This is the core of the topic. The God’s purpose was that Adam – through the keen observation of the animal habits (I think for a lot of months/years) he would be able to, not only nominate (i.e., to give a specific, peculiar name) every animals, but also to feel in himself the need of an apt mate for him (very different from the animal individuals).
So, the mention of the ‘formation’ (יצר) of the animals in Gen 2:19a is not a kind of ‘second animals’ creation account’, supposedly to complete the real animals’ creation account of Gen 1:20-25.
Nor, we may suppose the Hebrew verb here used (יצר) was in reference to a some body (material) structure of animals, as a counterbalanced term to the verb ברא (BRA, ‘to create’), as Dave claimed in his answer.
The verb יצר means ‘to form’, ‘to give a form (material or not)’. For some corroborations to this conclusion, we find in Isa 46:11, this term (יצר) linked with the God’s ‘plans’, or ‘purposes’ (surely not material!).
Again, we find in Jer 18:11 the term יצר as synonymous to מחשבה, this latter means ‘thought, design, project’. Also in this case, not some material ens.
Moreover, instead to be “two different, or distinct ‘steps’” of the animals’ creation – as Dave claimed – this Bible account points out to a different viewpoint the Bible reader has to adopt, helping us to understand a specific purpose of God.
This passage was a conceptual introduction (extracted from the real animals’ creation account of Gen 1:20-25) to justify the shift of the viewpoint the (Hebrew Bible) reader has to adopt at that point of the story-telling.
The purpose is to introduce the concept that man had need of an apt mate, very different from the other individual creatures yet present on the Earth.
As the psalmist sang:
“Thou, O Jehovah my God, hast multiplied thy marvellous works, and thy thoughts toward us: they cannot be reckoned up in order unto thee; would I declare and speak them, they are more than can be numbered.”
(Psa 40:5, Darby)