Transubstantiation is a Latin word consisting of trans (a transition or change) and substantia (substance, or what [makes a thing what] a thing is). Properly, then, it means 'change of what it is.'
This was naturally adopted by a Christians (the East use the Greek equivalent, however, metaousia), who believed that the words of consecration, "This is my body" were literally true of the bread, but not that this demanded the makeup of bread to disappear from it physically—it was a change by God of what the thing now is.
St. Cyril of Jerusalem's words sum this belief up quite well (Catechetical Lectures, 22):
For you have just heard him say distinctly, That our Lord Jesus Christ in the night in which He was betrayed, took bread, and when He had given thanks He broke it, and gave to His disciples, saying, Take, eat, this is My Body: and having taken the cup and given thanks, He said, Take, drink, this is My Blood. Since then He Himself declared and said of the Bread, This is My Body, who shall dare to doubt any longer? And since He has Himself affirmed and said, This is My Blood, who shall ever hesitate, saying, that it is not His blood? ... Consider therefore the Bread and the Wine not as bare elements, for they are, according to the Lord's declaration, the Body and Blood of Christ; for even though sense suggests this to you, yet let faith establish you. Judge not the matter from the taste, but from faith be fully assured without misgiving, that the Body and Blood of Christ have been vouchsafed to you.
As such, Catholics don't believe that Jesus' body is of one substance with the Father (but that the Son is). The Son is distinct from the body He assumed, given what this sentence just said. Nor do they even believe that Jesus is of one substance with His body (the Son and the body being conflated in such a case). They believe that the substance of the bread has become the substance of the body of Jesus, which is united to His soul and divinity (given that He is a real man with a soul, and the incarnate God).
In other words, they believe it is true when Jesus says, "This is my body" (not 'this bread' is my body; nor a game of charades).
(All accusations of 'cannabalism' will fall on deaf ears, too, when it comes to Catholics, since we know and have always known that there is no change in the accidents—the bread is the same to us before and after and to our body, physically. What has changed alone is the spiritual benefit when recieved, since "God has called" (Acts 10:15; Luke 22:19) it the Bread of Life, which is "[Jesus] flesh" (John 6:51). And so it is in all but appearance.)