Hardly. . .there is confusion here.
Not the same thing in the common usage of this non-Biblical distinction, where the "letter of the law" (not in Scripture) is said to be the literal (letter) meaning of the law, while the "spirit of the law" (not in Scripture) is said to be its "true deeper" meaning. . .none of which is the meaning of 2 Co 3:6.
The letter (law) is the true meaning (spirit).
The Holy Spirit does not impose a curse of death on disobedience, but delivers from the curse of death into eternal life and faith in Jesus Christ.
They are not the same--the law is the penalty, while the Holy Spirit is the remedy.
We are not ministers of the law which kills by its curse on disobedience,
we are ministers of the gospel remedy; i.e., the Holy Spirit, who sovereignly gives eternal life to whomever he pleases, and whose sovereign choice to do so is as unaccountable as the wind (Jn 3:3-8).