Photoshop :: Save For Web Vs Resizing Vs File Size Vs PNG

In playing around with some settings while saving a .png file, I noticed some weird results. For this example, the original image is 300 x 300, but I want the final size to be 200 x 200. I get different results depending on the order I perform the following operations (I never thought the order mattered until now).
 
1. start with 300 x 300 image, choose save for web, select png-24, with transparency, white matte, convert to sRGB, change image size to 200 x 200, then save - the file size is 37kb.

2. start with 300 x 300 image, use Photoshop's "image size" to change to 200 x 200, then save for web, etc - the file size is 111kb
 
So depending on which step I resize the image, the file size is significantly different - if I resize BEFORE using save for web, the file size is much larger. This is just weird to me, but I always resize AFTER choosing save for web, so that's why I've never caught this until now. In case you ask, while using Photoshop's "image size", all three options are checked at the bottom of that window, so nothing is getting re-sampled or anything like that.
 
The only thing I can think of is each of those methods treat pixel data differently when reducing the dimensions. When I overlay both exported .png files on top of each other, I see no difference in pixel quality and/or color shift - so why the big difference in file size? if I just save the file straight to .png, the sharpness is much better, and the file size is 46 kb. I did notice when saving for web, the colors become a little more saturated.I've never really paid much attention to the results when exporting .png's.