It is safe to assume that the Glorfindel mentioned in Lord of the Rings and the Glorfindel mentioned in the Silmarillion are one and the same. Aside from the idea that no two elves were to have the same name, Professor Tolkien was dedicated to making the two Glorfindels one, and that should be evidence enough. However, examining the lineage of Glorfindel can further support the idea of one Glorfindel.
It has been speculated that perhaps Glorfindel was from the line of Finarfin, since he does have golden hair. To accept this would be to cause problems for the two Glorfindels theory, since then you would have explain 1.) if either Glorfindel was related to Finarfin, why a second one with similar qualities (house of princes, etc.)? or 2.) If both are related to Finarfin, how can they have the same name? Of course, the latter can be ruled out as impossible. Yet even if you do assume that both Glorfindels are the same, you run into at least one problem: Why is he not on any of the lines of kings, or mentioned as related? I have looked for evidence of his relation to the line of kings in 8 volumes of the History of Middle Earth, and I have seen none. I have examined the Line of Kings, made by our very own Eru, to see if perhaps I had missed something. I have found nothing that would genetically link Glorfindel to the House of Finwe. It was common practice during medieval times to give such positions of authority to relatives or close friends (ex, Maeglin and Tuor becoming lords of Turgon's house, respectively), so the idea that Glorfindel is related is not totally implausible at first glance. However, since he must be related by Noldorin blood rather than Vanyarin blood (he could not be related through Indis since in LotR it says he is Noldorin) he should be on a line of Kings as related to Finarfin in some way. Most if not all of those related to Finwe in some way were stated as such in a story by the time Finrod (not Felagund) became Finarfin and Felagund became Finrod Felagund.
Second, I offer one example of the intricacies to which Tolkien worked on his lineages as an example of why if he were related to the House of Finwe he should be on one. I will cite the lineage of Aragorn's son, Eldarion. Through Aragorn, and thus through Elros, Eldarion is related to the house of Hador, the Haladin, the house of Beor, Melian the Maia and Elwe Singollo and thus one half of the Telerin House and also the Ainur, and the House of Fingolfin through Idril. From his mother's (Arwen's) side, he is related to not only those but also the line of Finarfin and the second half of the Telerin House through Celebrian, daughter of Galadriel and granddaughter of Finarfin. Both sides also give him a relation to Indis of the Vanyar, who was probably also royalty. The only royal house Eldarion is not descended from (purposely I believe) is the house of Feanor.
If we take this as evidence that Glorfindel is not related to the House of Finwe (more specifically Finarfin), how could he both be a Noldo and have golden hair? I cite two quotes in order to help me answer this question.
"Alone among the Noldorin princes he and his descendants had golden hair."Both are from the Silmarillion. The first citation comes from the index, in the description for Finarfin. The second is found in the section called "Of Eldamar" (pg 59 of the Houghton Mifflin hardback).
"In Tirion upon Tuna the Vanyar and Noldor dwelt long in friendship."
My conclusion: Finwe was not unique in being a Noldo that married a Vanya. It may not have been a common practice between the Noldor and Vanyar, but while living close to each other for many centuries, it no doubt happened between more than just Indis and Finwe. It is interesting that only Finarfin and his line ended up with gold hair, despite Fingolfin also being a son of Finwe and Indis, and his line was unique among the other princes and indeed the Noldor as a whole, but that does not mean other Noldor did not marry Vanyar. Also, as I have said before, one need not be related to get a position of authority (a lord can also be a close friend), the father/mother/other relative of Glorfindel could have been a friend of the house of Finwe, though Glorfindel would most likely have had a Noldorin father. Glorfindel then would've become a friend of Turgon, or perhaps his father was already a lord in Turgon's service, who died in battle, died on the Helcaraxe, or stayed in Aman. These all end with the same result, the Noldorin lord Glorfindel and his golden-haired house.
Lord of the Rings
History of Middle Earth Volumes 1-8
Line of Kings by Eru-(Valar)