The pads that certain suppliers often call "standard", are approx .185" thick. I have a complete inventory of them, and almost never use them. A well-established local colleague regards his stock as so dead that he has recently sold the lot. These pads are less than suitable for MOST saxes, because pads this thick will almost always close at the "back" of the tone hole before contacting the front, unless the front is packed out with glue used as a filler.
On the other hand, what is often described as "thin" is approx .165" thick, and are what I use for almost every instrument.
I think this is probably the experience of most serious technicians.
So the reality is that I have come to regard the .185" pads as "thick", and the .165" pads as "standard", because according to use, that is exactly what they are.
Some saxes do not have a lot of spare space for keys to lift higher than they were designed to lift. For such saxes, irespective of brand name, the result of installing over-thick (.185") pads is bad. Either a lot of glue is needed at the front as packing, or the keys need to be be tilted forward to accommodate the extra thickness. Either approach reduces venting, which cannot be corrected if the key cannot lift higher without hitting another part of the sax. This adjustment to accommodate over-thick pads is becomes ridiculous if the key cup arms are unusually short on a particular model of sax - because of the whole geometry of the key, without going into detail and drawing diagrams.
Perhaps this is why this discussion has been unfortunately hidden away in the Martin section of the forum rather than in the Tech section. Martins are by no means the only saxes to have unusually short key cup arms.
BTW, IMO such short arms are an extreme deviation from the theoretical ideal of having pads lift vertically from tone holes, and as such, represents a lower standard of mechanical design, but don't tell Martin enthusiasts that!
So may I suggest that this discussion may be little more than a semantic one. Normal, standard (.165") pads, which some suppliers unfortunately call "thin", are used for all saxes unless there is a particular reason for using thick (.185") pads, which many suppliers unfortunately call "standard".
The names given for thickness are really quite arbitrary.
Perhaps it is pertinent that Music Center (world's largest pad maker, previously Pisoni) in Italy, lists the following thicknesses for their standard range of pads. (They actually make any thickness to order):
Thick: 4.5 mm (i.e .177")
Medium: 4.3 mm (.169")
Thin: 4.0 mm (.157")
Very Thin 3.8 mm (.150")