Are the Colt .38 Automatic and the Colt .38 Super Automatic + P the same cartridge? Are they interchangeable?

The dimensions of the cartridges are the same. But I would not stick a 38 super plus p to n a 38 colt pistol.

38 super plus p and 9mm plus p are almost identical with
124-125 grain bullets. That being 1240-1250 at the muzzle from 5 inch barrels.

If I am wrong someone correct me.

I'm not familiar with the +P version. Originally there was 38 auto. Later they introduced the 38 Super auto .Same dimensions but higher pressure . This situation was the same as the 22 RF Standard velocity vs the 22RF High Velocity. The high velocity versions would damage the standard ones in time. The Colt 22pistols were marked so you could easily see which one you had !
Like the frequent use of 357 loads in a S&W K frame .
Hotter loads won't blow it up but will pound the gun very badly !!

The 38 super is a much higher pressure round than the 38 auto. Same dimensions. Way different result. Keep your fine old 38 auto in one piece.