Unfortunately, the definitions are kind of relative.
They are both types of patterned glass, made by rolling the still hot glass under patterned rollers during the final stages of manufacture.
As such, of course, the exact pattern varied according the the manufacturer - even the size or scale of the pattern elements can vary quite drastically. What is available now will almost certainly NOT match what was available then.
That said, generally "pebbled glass" has a pattern that looks something like as if tiny spherical balls of varying size were briefly pressed into the hot glass and then removed, or pressed in and left to become part of the glass. This generally means more or less round dimples in the glass or little round hemispheres sticking out of the glass, respectively. Can also be slightly oblong and a bit irregular, more like natural stream pebbles, but still usually with clearly defined edges and slight gaps between.
In contrast, "hammered glass" more properly refers to a pattern that is suggestive of the very old method of actually gently taking a hammer to one side of the hot glass to create small, relatively shallow dish-shaped impressions with some overlap so that you have a semi-regular pattern of IRREGULAR depressions. The craters produced can be smooth bottomed or quite bumpy, depending on the effect desired by the manufacturer.
On the suggested site, that is a fairly strong version of "hammered glass" in that it is DEEP in the depressions and almost like a cross between hammered glass and pebbled glass. Of course, it's 1/8" glass and subject to breakage and there is no clear idea of the scale of the pattern.
Similar patterns have at various times been available in perspex - of course, good luck in finding it.
All that said, it seems the impression I get in most of the pics posted here and elsewhere of actual boxes is that they usually come off as "pebbled" despite the Trench plans specifying "hammered" (I note that in the Crich box pics it appears to have both types in different locations, possibly taken at different times).
Most of the TARDIS pics seem to show it with more of a pebbled texture, though the McGann TARDIS is closer to a true "hammered" glass.
Oh, while on the subject, I do recall back in the day seeing at least one pic of the old series TARDIS at some point or another having a glass pattern identical to the McGann TARDIS right door, though it may have been a window in one of the side panels.
) and trying to find the right references can be a real challenge. I found the season 18 prop photo you posted:
