I agree with this. I know some Pentecostals try to make tongues for prayer and tongues to be interpreted into a different 'type' of speaking in tongues. But the wording of I Corinthians 14 treats them as the same category of speaking in tongues, as if the tongues that are mysteries that can be spoken to God can also be interpreted.
You're right that Paul treats tongues as one category of gift. There aren't "two different kinds" of tongues - but Paul does distinguish two different uses of the same gift:
Private use - prayer to God (unintelligible without interpretation)
Paul says: the tongue‑speaker "speaks not to men but to God" (14:2), no one understands (14:2), my spirit prays, but my mind is unfruitful (14:14), "he speaks mysteries in the Spirit" (14:2), "he edifies himself" (14:4). This is the prayer‑tongue use - same gift, but not intelligible & not for the congregation.
Paul even says he "speaks in tongues more than you all" (14:18), showing his heavy private use.
'Public use — must be interpreted. Paul commands:
"let him pray that he may interpret" (14:13), if there is no interpreter, let him keep silence in the church" (14:28), "let all things be done unto edifying" (14:26). Same gift - but regulated so the church is edified.
Paul's point is simple:
Tongues without interpretation = private prayer.
Tongues with interpretation = intelligible message (equivalent to prophecy).
So yes, it's one category of tongues - but Paul gives 2 different instructions depending on whether interpretation is present.
That's the distinction many Pentecostals often blur & the one Paul makes repeatedly in the chapter.