You're using ambiguous and generic imprecise terminology, which is adding to your confusion.
Regardless of whether a disk drive is (a) installed for use internally inside of your PC case and then connected to the motherboard with a SATA data cable as well as to the power supply with a SATA power cable, or (b) installed for use externally inside of a separate physical enclosure and then the enclosure is connected to wall power with a 12V power adapter as well as being connected (for "data") to a USB port on the PC through a USB cable, there are two aspects of that disk drive which determine whether (a) it is physically seen by the hardware and if so what are the physical characteristics of the drive, and (b) has the drive been "formatted for use" and if so how and what are the current contents of the drive, if any, both allocated "in-use" as well as unallocated "free space".
The physical characteristics of the drive include the manufacturer's model number, perhaps firmware version for the drive, total capacity of the drive in bytes, etc. In order to support access to the data bytes available on the drive, a "partitioning method" is used. This "partitioning" is a technique by which the total physical capacity of the drive can be sub-divided into smaller "partitions", which might be thought of simply as smaller independent "logical" drives all of which together constitute the one large physical drive.
In order to specify how the physical drive is sub-divided into one or more "partitions" (i.e. smaller "logical" drives) one of the two standard partitioning techniques or methods is used (either MBR or GPT, the details and differences of which aren't important at the moment). A small portion of the drive is reserved for use by MBR/GPT in order to store the "partition table" which contains the low/high sector number for each of the one or more partitions on the drive (where "sector" is the "address of" a specific collection of bytes on the drive, equivalent to identifying a particular location on the disk).
As is clearly visible in your screenshot of the "non-working" situation, the drive inside the enclosure shows TWO PARTITONS: one is the 6GB partition (shown as "healthy (OEM partition)", and the other of which is a 180GB partition (shown as "healthy (active, primary partition)". This says lots of things, all of which are GOOD. First it says that the "partition table" on the drive is present, in good shape, and visible and readable by the computer BIOS hardware which has passed the low/high sector information for both partitions to DISKMGMT.MSC for presentation in this window. We see on the left that there is 186GB of "formatted capacity", which suggests to me that this is actually most likely a 200GB raw byte capacity drive, with 14GB of it having been used up to create "sectors", partitions, etc., leaving the remaining 186GB for sub-division into one or more partitions. In your case TWO PARTITIONS were created 14 years ago, and they are still physically "visible" by the PC hardware and DISKMGMT.
The second aspect of EACH OF THE ONE OR MORE PARTITIONS on the drive is the "internal data contents" on that partition. This pertains to allocated folders, sub-folders, and files, as well as unallocated free space. All of this information is catalogued in a "Table of Contents" through and organizational method named the "file system" for that partition. In order for Windows to be able to use and manage the data contents of any partition, every partition MUST HAVE A FILE SYSTEM on it (i.e. "table of contents for that partition"). If there is no "table of contents" (i.e. "file system") present inside the partition, Windows has no way to know what folders/sub-folders and files are, where they start and end, what their names are, what date they were created/modified/accessed on, who created them, etc..
Although it should normally never be the case that a partition exists without also having some "file system" present inside the partition which provides the "table of contents" for that partition, that appears to be the case fo your problem drive. That's proven by the screenshot from DISKMGMT which has blank space up in the field of the "file system" column for the two partitions. That is impossible, and yet it is true. How did that happen? I don't know. Might it indicate a physically defective drive, whose electronic ability to read/write data might have gotten fried, so that the "file system" table of contents is simply no longer readable? That's possible too.
Might there be some other logical reason why the "file system" has disappeared (since it HAD to be present originally when the drive got partitioned, as creating an empty "table of contents" on that partition is just something which is automatically always performed when partitioning a drive? Yes as well. When that 180GB partition got created, its "file system" also had to have been created. But it's not there now and we will never know how it disappeared. There's no real Windows authorized method for vaporizing a "file system". You simply can't do it. And yet... we know it's currently now gone. Somehow. But in truth it is gone.
In contrast, it's obvious that your 320GB Seagate drive is "working properly", and that NTFS shows up as the "file system" for its one partition. And because Windows can read the "table of contents" for that partition on the working Seagate drive, Windows went ahead and assigned a drive letter (of D) to it. And that's why you can access the folders/sub-folders/files on that D partition when the Seagate drive is in one of your several enclosures... because (a) the partition table is in good shape, and (b) the NTFS file system is in good shape.
But for the defective 200GB drive has what might be an otherwise usable 180GB partition on it, but the "file system" has somehow gotten vaporized, for reasons we will never know. And that's what makes this drive UNUSABLE BY WINDOWS AT THE MOMENT, because there is no "file system" present. The drive is apparently powered up and spinning, and the partition table is present so that the drive shows up in DISKMGMT.MSC, but because the "file system" has somehow been disappeared the partition is unsuable for Windows. Hence Windows does not assign a drive letter to that partition, and you cannot access it through Windows for purposes of "data".
However... all you have to do is re-partition this 200GB drive today, using Partition Wizard (or DISKPART, or any other available technique), and there is a possiblity we can bring the drive back to usable useful life. As long as the drive itself has not truly been electrically fried and thus is now truly defective and physically unusable, if the drive still really works and we can re-partition it from scratch (and thereby also reinstall an initialized empty NTFS "file system" table of contents on that partition) then the drive should magically spring back to life immediately thereafter.
Just use Partition Wizard to DELETE the two partitions currently on that physical drive. This will produce 186GB in total of "unallocated" free space. Then use Partition Wizard to CREATE let's say just one new partition (opting for NTFS as the file system), using up all of that 186GB free space and assigning a drive letter of D to that partition. All of this can be done by Partition Wizard when you then push the APPLY button.
30 seconds later, you will have this drive usable for you again, because we've now re-partitioned the drive to use all 186GB for one new partition, and also simultaneously installed an initialized proper NTFS "file system" on it. This completely satisfies the Windows requirements, and you're now in business (with either of the first two enclosures you bought), just like with the Seagate drive.
Hope this wasn't too dramatic. But if you simply follow my instructions and use Partition Wizard, this whole story will be over in under 1 minute from now.