PS2017.1 file resolution and printing

Some details (including settings) of exactly how you are doing your resizing would be helpful.

When you resize as described, without checking the 'resample' button, nothing is changed in your pixels. The in/cm size is just a text note to show you in advance the resulting resolution when printing, it's just a note of your 'printing intent'.
If the pixels are not changed, that means that the process can't produce artifacts on the pixels.
Since you are seeing a difference, the very common issue may be with the display on your monitor. To judge the difference, you should set the display to 100% view, a screen pixel equals a picture pixel - shortcut double click on the magnifier tool.
The other way would be to print both versions on a 4 x 6 " paper, setting the printer paper size to that dimension and to fit in that paper. You should not see any difference (you would be above 300 ppi).
Anyway, if the purpose is to display on the web, the physical in/cm dimensions are totally irrelevant, only pixel dimensions are significant.

As a matter of fact, 300 is too much, even for offset printing according to JR_Boulay, 240 is good enough. So, it's even easier here where we are using metric units: we just divide by 100 to get the possible size in centimeters. (one inch = 2.54 centimers).
forums.adobe.com/thread/2162809

For instance, for A4 (21 x 29.7 cm), 2100 x 2970 pixels is a good estimation.

Yes, Janice, we totally agree and I'll never get tired of repeating that only pixel count is important.
That said, since you mention scrapbooking, it's a bit a special case for two reasons: it's always about printing, and the print size is nearly always 12" x 12" (30 cm x30 cm). So, scrapbookers do use the same language.
I do print books at the 12" x 12" size, using about the same techniques as scrapbooking for manual page layouts.
The viewing distance is the second important factor. Viewing prints of that size and resolution from two feet is very good. My camera provides 4896 x 3264 pixels. That's more than needed and is still adequate for a background image covering two pages with full bleed.

Sepiana,
There is nothing really different with scrapbooking, the same rules do apply for printing. Yes, 300 is recommended everywhere and especially by online labs: it's too much but 'overkill' may be somewhat exagerated. But I think no lab would take the risk to say '240 is enough'; that would be automatically negatively misinterpreted. My point was that even if pixel size is the important factor for any kind of output, you have to take resolution into account when printing. Printing is always the case with scrapbooking. Since the size is always fixed, everybody has the 12" and 3600 pixels limits in mind; easy to add new elements to the layout.
From my experience, most of the posters writing about the '300 ppi myth' are not photographers, they are professionals dealing with printing and softwares like InDesign. They do know what the printing tools are able to achieve. They also can explain that the default 300 ppi requirement came historically from outdated softwares like Quarkexpress.
I have also a possible historical explanation for photographers. I started digital in 1999 with a 1.4 MB Fuji... hardly good enough for 10 x 15 cm prints. Today, any basic camera has 12 MB, even smartphones try to compete in that megapixel race. The common understanding has been that more pixels meant bigger prints; printing a 20 x 30 cm would require an 8 Mpix camera (like my old Canon 20D, rather than 6 Mpix from the 100 pp/cm). That was to allow for some cropping and for the loss of sharpness from the Bayer interpolation in sensors. Maybe that has justified an increased resolution for printing too...
It's not difficult to print test photos at home or from online or local labs. Choose quality glossy paper and compare with a magnifier.