Yes and no.

It's one part semantic and one part obfuscation.

John the Baptist said he washes Man with water, but one will come who will wash Man with the fire of the Holy Spirit.

Some denominations take that two ways, others include it in the same Rite.

What you may call a Baptism is actually a consolidation of Baptism and Confirmation. Before the Reformation, they were separate sacraments in the vast majority of congregations.

In Orthodox, Catholicism, and Episcopalian denominations it is still this way.

For them, Baptism is the reception of the Holy Spirit, which cleanses the soul of Original Sin. We can debate what Original Sin is, but in short it's just the fallen nature of Man to put the SELF before all other things, namely God (Love). This is in line with John the Baptist's actions and critical message of Repentance.

Confirmation is the personal acceptance of the Holy Spirit, much like in the way you depict Baptism. It is performed at Pentecost, in line with when the Apostles received the tongues of flame above their heads and began to speak among the people in the universal language of Truth. This is in line with Jesus' promise that he shall not leave us as orphans.

In summary, the debate is lamentably semantic. I hold neither interpretation in higher esteem, but I have my preference, if only because it is the careful option.

Just because you can do two steps in a LEGO instruction manual at the same time, doesn't mean you HAVE to. It also doesn't mean you DON'T HAVE to either.

But...

If we go by chronology, Baptism being for cleansing the young of their Original Sin and Confirmation being the acceptance of the Holy Spirit (and the mission of spreading the Good News of our Savior, Jesus Christ) has been around longer.

Spiritually, however, I will readily concede that Baptism Rites undergone by Protestant denominations are far more spiritual and life-changing than the suffocate-ingly formal sacrament of Confirmation.

Either way, there are still those who grow up "in the Faith" that aren't truly Christian, regardless of denomination.

They go through the motions mostly due to peer pressure and because they've known nothing else their entire lives. Some could say that THAT is the Original Sin, as it is the proliferation of the "Sins of our Father" (Adam) being forced upon our young -- coercing them to believe what we do, flawed or not, rather than encouraging them to find the Truth on their own with careful guidance.