MW- I don't want to discuss the pros and cons of L-J. The OP had asked this:
the Westminster view opened the door for the “second blessing” theology which developed later among some Protestants. So can someone explain these differences of Assurance more deeply to me please? And what is 2nd Blessing Theology?
I think- mind you I am not nearly as well educated in this fairly recent church history as some others may be- that M L-J may be a significant answer to the OP's question.
Here is the link to the "Calvinist Methodist Confession of Faith or the Presbyterians of Wales" ( 1823):
( note it was for both Welsh Methodists and Presbyterians and I have no what Presbyterians adopted it and what influence they had in Great Britian, and don't have time today to research, but I post it as a possible lead for the OP).
http://www.creeds.net/cmwales/main.htm
snip: ( highlight is mine).
33. Of the Assurance of Hope.
The assurance of hope follows upon true peace of conscience and a strict walk with God by faith. Hypocrites may deceive themselves with false hope and a carnal presumption of being in the favour of God and in a state of salvation, but their hope shall perish (a). But all that believe in Christ, and love him in sincerity, and endeavour to walk before him in all good conscience, may, in this life, be certainly assured that they are in a state of grace, and may rejoice in the hope of the glory of God; and their hope shall never be put to shame (b). This is not a doubtful conjecture, grounded on a false and feeble hope : it is "the full assurance of faith," resting on the blood and righteousness of Christ, as it is revealed in the gospel; an inward evidence of saving grace in the soul; and the witness of the Spirit to their adoption. The effect of this assurance is to make their hearts more humble and holy (c).
A true believer may have to wait long and strive with many difficulties before he enjoys this assurance (d); but being enabled by the Spirit rightly to use the means of grace and divine ordinances, and being taught to know the things which are "freely given him of God," he can attain it without a miraculous revelation of any kind (e);
and it is the duty of every Christian to give all diligence to make his calling and election sure, that he may largely experience the love of God and joy in the Holy Ghost, and more boldly, usefully, and cheerfully walk in the path of duty (f). The Christian's assurance may in divers ways be shaken and impaired : if he falls into any sin and grieves the Spirit, he loses the light of God's countenance, and walks in darkness (g). But the Christian can never lose that seed of God which is in him, or the life of faith, or the love of Christ. The Spirit restores him in God's good time, and meanwhile keeps him from utter despair. The evil of his sin is revealed to him, and he is chastened by the Lord, that he may not be condemned with the world. But he is strengthened in all his affliction to hope in God; yea, he has hope in his death (h).
Here is the WCF; you can see how alike it is:
http://www.reformed.org/documents/w...body=/documents/wcf_with_proofs/ch_XVIII.html
This infallible assurance does not so belong to the essence of faith, but that a true believer may wait long, and conflict with many difficulties, before he be partaker of it:[10] yet, being enabled by the Spirit to know the things which are freely given him of God, he may, without extraordinary revelation in the right use of ordinary means, attain thereunto.
[11] And therefore it is the duty of every one to give all diligence to make his calling and election sure,[12] that thereby his heart may be enlarged in peace and joy in the Holy Ghost, in love and thankfulness to God, and in strength and cheerfulness in the duties of obedience,
[13] the proper fruits of this assurance; so far is it from inclining men to looseness.
[14]
I am not Iain Murray and I don't want to pretend to speak well for L-J, but I think what L-J was trying to say was what is in the WCF and the CMC. You might wait long to have assurance, and may need to diligently pray and seek God until you know for certain with full assurance that salvation belongs to you. L-J did believe in an experiential reality of that love, joy, and assurance, and would call it a baptism in the spirit for those who go from doubt and fear to the solid unwavering conviction. So he did believe in subsequent spirit infilling/baptism/outpouring- but he did not equate it with the Acts event of the disciples praying in other tongues unknown to them but understood by foreigners.
Anyway, L-J was very influential on Presbyterians, by himself and with Iain Murray, and I am trying to answer the OP and not argue about L-J. I do happen to think these experiences can be perfectly in line with biblical NT teaching but that isn't what the OP is asking. He is trying to figure out where any WCF second blessing influence on Presbyterians came from and I am offering a possible explanation.