Joh 13:34 A new commandment I give to you, that you love one another; as I have loved you, that you also love one another.
Joh 13:35 By this all will know that you are My disciples, if you have love for one another.
Lev 19:18 You shall not take vengeance, nor bear any grudge against the children of your people, but you shall love your neighbor as yourself: I am the LORD.
Lev_19:34 The stranger who dwells among you shall be to you as one born among you, and you shall love him as yourself; for you were strangers in the land of Egypt: I am the LORD your God.
Same stuff. What's NEW is it's application...a spiritual love that surpasses physical love that can only exist under the new covenant. John sums up this "new" commandment:
The New Commandment
1Jn 2:7 My dear friends, I am not writing to give you a new commandment. It is the same one that you were first given, and it is the message you heard.
1Jn 2:8 But it really is a new commandment, and you know its true meaning, just as Christ does. You can see the darkness fading away and the true light already shining.
1Jn 2:9 If we claim to be in the light and hate someone, we are still in the dark.
1Jn 2:10 But if we love others, we are in the light, and we don't cause problems for them.
Same stuff.
No, it is not the same stuff.
Your neighbor is not your brother.
Your fellow faithful disciple is your brother, more even than another issue of your mother's womb, should he/she be unsaved and content in that state.
Your neighbor is your enemy, still obedient to the god of this world, sometimes bitterly so. You cannot love them with disciple love, for they do not have the spiritual faculty to receive it, sadly.
Respect and love them as a neighbor, yes; but as a brother/sister in Christ, not possible.
And that is why John's Gospel is written to the neighbor, in a loving way (Jn. 20:31), but John's first epistle is written only to those born-again believers whom he can call "brothers" (1 Jn. 1:3,4; 5:18-20).
So don't misapply them, as does the paraphrase you cite here. And I may say, if a citation is to be made, let me suggest that you acknowledge it, or it will just be taken as your opinion, not as the infallible inerrant, verbally and plenarily inspired preserved and faithfully translated Word of God.