Question: Did people in the Old Testament go to Heaven the same as Christians do today?
Answer: No, the saved went to "Abraham’s Bosom" (a Jewish term for Paradise); and the lost went to Torment, both located in the center of the Earth. Luke16:19-31 describes the two places. Matthew’s prophecy concerning Christ lets us know that Paradise is in the center of the Earth.
In Luke 23:43, Christ is speaking to the thief next to Him, who had acknowledged Him as the Savior. He said, "Today shalt thou be with me in PARADISE." Matthew 12:40 lets us know the location of Paradise,
"For as Jonas was three days and three nights in the whale’s belly; so shall the Son of man be three days and three nights in the HEART OF THE EARTH."
After Christ’s Resurrection, He appeared to Mary and said,
"Touch me not; for I am not yet ASCENDED to my Father." (John 20:17).
At this time Christ ascended to Heaven and anointed the Mercy Seat within the Holy Place with His own blood.
Hebrews 9:12 states,
"...But by his own blood he entered in once into the holy place, having obtained eternal redemption for us."
He then returned to Earth and walked 40 days before His final Ascension. (Acts 1:3, 9-11).
At His Ascension, he emptied the saved out of Paradise in the heart of the Earth, taking them to Heaven with Him. Ephesians 4:8 makes this clear:
"Wherefore he saith, When he ascended up on high, he led captivity captive, and gave gifts unto men."
Paradise is no longer in the center of the Earth, but is now in Heaven. This is revealed in 2 Corinthians 12:2,4 which describes a man,
"...such an one caught up to the third heaven. How that he was caught up into paradise..."
With this in mind we can understand what Christ meant in John 14:2 when he stated:
"In my Father’s house (Heaven) are many mansions: If it were not so I would have told you. I go to prepare a place for you."
He didn’t go to build the mansions. The use of the word "are" reveals the mansions were already there. He went to the Cross, shedding His sinless blood; then, ascending and anointing the Holy Place, thus preparing Heaven to receive the saved. Ephesians 1:7,
"In whom we have redemption through His blood, the forgiveness of sins, according to the riches of his grace."
Now we, like Paul, can say,
"We are confident, I say, and willing rather to be absent from the body, and to be present with the Lord." - 2 Corinthians 5:8
When a Christian dies, today, it is just "a change of atmosphere." The soul and spirit, the real "You," goes immediately to Heaven to be in the presence of the Lord. The body goes to the grave to await the Rapture. (1 Corinthians 15:51-53; 1 Thessalonians 4:13-18).