The text of the vast majority of the manuscripts (the Majority Text) differs from the TR in nearly 2 000 places (1838, according to Professor Daniel Wallace of Dallas Theological Seminary - 'Studies and Documents', Vol.46, p302, footnote 28). It might be better to say that the TR is similar to the Majority (or Byzantine) Text, but it is not the same.
The TR includes some verses which are found in virtually no Greek copies. These verses include Luke 17:36, Acts 8:37, Acts 9:5b-6a and Acts 15:34. How did they get into our Bibles? These verses were incorporated into the NT by Erasmus from the Roman Catholic Latin Bible.
Perhaps the most famous problem with the TR is found in 1 John 5:7-8.
Erasmus' first edition was criticized for not including in his Greek NT the words about there being 'three who bear witness in Heaven: the Father, the Word and the Holy Spirit, and these three are one'. He included these words in his third edition after this criticism, however, these words are only found in Latin MSS of the NT and a handful of very late (i.e. 16th and 17th century) Greek MSS.
1.) "the" Majority Text is a compilation of extant, Greek [only] manuscripts, and it's possible that said compilation/collation only involved some 200 or so manuscripts. The evidence for the readings underlying the KJB comes from a much wider and more varied set of sources than just Greek manuscripts (and includes old versions, lectionaries, quotations from the church fathers, etc.). [The foregoing statement would deal with the OP's "virtually no Greek copies" comment, as well as "handful". Furthermore, the age of the MANUSCRIPT is not the most fundamental issue, but rather the age of the READING -- Burgon deals extensively with the foregoing issues in his book, The Revision Revised.]
2.) There are at least 3 or 4 editions of "the" Majority Text and they all differ among themselves, as well as from the readings underlying the KJB.
3.) There is no "the" TR -- there are about 30 editions of TR family texts which differ some among themselves, and all of which differ to one degree or another from the readings underlying the KJB. So Wallace's or anybody else's grousing about "differing from 'the' TR" is really a bit disingenuous.
4.) Every available published edition of a Greek N.T. [TR family or not] differs in some places from the readings underlying the KJB. In other words, as far as I know, there is no available published edition of a Greek N.T. which is all the exact readings underlying the KJB. Consequently, any grousing about "differs from 'the' TR" is really irrelevant.
Now if one wishes to say, " 'x' edition of 'the' Majority Text, (or 'x' edition of a TR family text) differs from the readings underlying the KJB in 'x' number of places, that'd be fine.
Now to answer the question as to "how these verses got into our KJB", there are two basic answers:
1. God put them there via His preservation of His words -- Psa. 12:6-7.
2. The 47+ learned men, plus all their consultants, plus their meticulous review procedure, all concluded that the readings underlying the KJB are the best attested readings and were used as the basis for the KJB translation.