Both Matthew's gospel and Luke's have this statement about Jesus being led in chapter 4 verse 1 of their respective accounts. Strangely, I cannot find either listed in Young's Analytical Concordance, under the word 'led'. This caused me to check his literal translation.
Matthew clearly states that the Spirit of God descended on the newly baptised Jesus:
"Then Jesus was led up to the wilderness by the Spirit, to be tempted
by the Devil." Young's Literal Translation, Mat.4:1
"And Jesus, full of the Holy Spirit, turned back from the Jordan, and
was brought in the Spirit to the wilderness, forty days being tempted
by the Devil." Ibid., Luke 4:1
I then remembered a lecture from a New Testament scholar (some years ago) who said that Jesus 'being led' used a word that denoted a forceful driving by the Holy Spirit. I could not find any mention of this action of the Spirit in any of his five books about Christ. Nor did Young have either Matthew 4:1 or Luke 4:1 listed under 'drive' or 'driven' etc. in his Concordance.
However, the grammatical aspects already explained in the answer with the Green Tick show that the same Holy Spirit, or, Spirit of God, that had just been displayed in the form of a dove, was the Spirit that immediately got Jesus into the wilderness, for the express purpose of the Devil being given opportunity to try to tempt him. That just leaves your secondary question, about James 1:13-14, to be addressed.
James was writing to Christians, starting with a warning to be on their guard as to the true nature of succumbing to sin when they were tempted. Young's translation again:
"Let no one say, being tempted - 'From God I am tempted,' for God is
not tempted of evil, and Himself doth tempt no one, and each one is
tempted, by his own desires being led away and enticed, afterward the
desire having conceived, doth give birth to sin, and the sin having
been perfected, doth bring forth death." Ibid., James 1:13-15
God does not tempt anyone with evil, so the Spirit that led Jesus into the wilderness was not leading him in order to be tempted with evil by God. The evil temptation was by the Devil. That is because there was no sin in Christ. Had not God just declared that Jesus was his beloved Son, in whom he delighted? (Matt. 3:17.) Jesus, being God incarnate, had no evil desires in him. The Devil knew that there was no sinful desire in Jesus that he could work on. That is why he used the Father's own words, forty days earlier, to get Jesus doubting what the Father had told him - that he was the Son of God. The first two temptations tried that tactic. After all, that had worked with the woman in the garden before she sinned - he got her doubting what God had said.
This shows how radically different the temptation of Jesus by the Devil was to the kind of temptations James was warning Christians about. The Devil is not even mentioned by James in this respect. The temptation comes from within the person, from their own sinful desires. Chalk and cheese differences here. The text quoted in James does not apply to this question about Jesus.