First off, don’t worry, you have not fallen victim to some massive Bible destroying conspiracy. There are basically two different families of English translations. You have the King James Version/ New King James Version and on the other side you have the English Standard Version, New American Standard Version, the NIV and others. All of these versions are fairly accurate translations, although some are more accurate than others.
As archaeological discoveries are made we are able to find older and older manuscripts. It is assumed that the older the manuscript, the more accurate to the original it is. When the King James Bible was formed the manuscripts the translators used were not as old as the ones that formed the New American Standard Bible and others. Over time when copying by hand verse endings may have been added or footnotes may have been mistakingly copied as part of the text. This is why you will sometimes see verses in one Bible and not in another. It is not that the newer versions took them out, but that as older manuscripts are found, we discover a more accurate rendering of a passage.
None of these variant passages are significant when it comes to doctrine. Even with the differences, there are no key teachings removed or added, and in the grand scope of Scripture they prove to be very insignificant. You will notice that in your Bible usually there will be a footnote explaining why a verse is not in your particular translation. For example in (Acts 8:37) you may see a note saying “NU, M omit v. 37. It is found in Western Texts including the latin tradition” (Nelson NKJV).
The translators of our English Bibles are very transparent when it comes to why a verse is removed or added. It can be a very rewarding study to research the origin of our different English Bibles.