You are correct. If you drag an object to change its size or shape using the Transform function, (Edit > Transform > Scale) in Photoshop, you are in effect "stretching" the object rather than modifying its shape. Curves and rounds will deform and become ovoids in the process.

So, in order to change the aspect ratio of an object which was drawn with the Shape Tool, or Pen Tool, you'll need a proven rule learned by Illustrator users since the dawn of QuickDraw and PostScript vector objects in the mid 1980s.
Use the Direct Select Tool
Here, you will use the Direct Select tool (the hollow pointer, tap "A" or "Shift/A") with the active path, and select just the anchor points you need to 'move' in order to change the aspect ratio.
In this diagram, we've used the Direct Select tool to drag a selection marquee around just the right-hand anchors. Notice THEY turn solid. This is your visual indication that they are selected.

Once selected, you can drag any one to move the selected "set" of anchors into the new position. Notice they retain their perfectly round aspect-ratio, while your shape is not the size you desired.
RULE: The SOLID pointer tool will select ALL anchors -- Solid tool = Solid anchors.
The HOLLOW pointer tool selects individual anchors or paths -- Hollow tool = Hollow anchors.
RULE: If you wish to change the aspect ratio of any vector shape, while retaining the integrity of the anchor positions themselves, you MUST select the target anchors, and move anchors as a group, rather than transforming the whole object.
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from the Editor:
I was delighted that day back in 1989 when Peggy Killburn called to ask if I could handle one more speaker in my "Great Graphics Tips & Tricks" session scheduled for the 1990 Macworld Expo. "Yes" was my response to her request to add Russell Brown to my panel. After all, we loved Adobe's young "Illustrator" program, and were quite anxious to try out their upcoming new product called "Photoshop." After seeing his demo, I was convinced Photoshop would be big. So the next month we added "Photoshop Tips & Tricks" to our regular DTG Magazine uploads to Compuserve, GEnie and AOL. The rest is history.
I only regret that I didn't trademark the name.
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Editor / Publisher: Photoshop Tips & Tricks, DTG Magazine.