Deck screws, construction screws and wood screws are not rated and not permitted for structural work.
The shear strength of general unrated screws does not suffice to withstand live loads with additional dynamic loading and movement due to wind and earthquakes. Framing nails may bend while construction screws may snap.
There is a use for construction screws in load bearing applications, though, which is to pull lumber tightly together or hold it in place so that it can then be nailed to spec.
If you want to fasten structural members, you should use framing nails or structural / framing screws for framing elements. Here is an example:

For headers, beams, joists and load bearing walls, use the above.
Alternatively use 10d framing nails:

(Building codes specifically mention nail strengths (8d 10d etc..) and nail patterns, and it is up to the manufacturer of screws to rate and test their screws to replace such nails.
The above framing screws are different from construction screws such as this one, which is not rated for structure:

Deck screws are sometimes available at a lower price than wood screws but they are equally not allowed for structural work:

So depending on where you used these screws they may have to be replaced or supplemented.
Do not use wood or construction screws for joist hangers, beams or headers / lintels.
You can use wood & construction screws for fastening windows, doors, strapping, furring, bulkhead boxes etc...
I have seen studs fastened to the plates with wood screws, which I believe is allowed in non load bearing interior walls. In these cases you could use coated wood screws a.k.a deck screws. There's no need for the coating indoor, but sometimes they are cheaper.
There are various reports and documents available online that should cover this. See the ICC-ES ESR-3201 report from this year on GRK screws or the same document, but embedded in ICC-ES's website.
The tables from the ICC-ES documents are too large and comprehensive for me to transcribe here, but as official documents from code governance bodies, those links should be reliable... here is a screenshot of one of the first tables, which includes shear strength for various screws, including the R4 model you mention in your question:

And from GRK's own webpage on compliance:
Having an ICC-ES ESR report means fasteners have ICC approval. GRK fasteners are ICC code approved for exterior use in ACQ pressure treated lumber and have the strength to meet all your general construction needs. A building inspector will be able to use an ESR report to code approve your construction projects.
[...]
- ESR 3201: R4 multipurpose screw, FIN/Trim screw and Kameleon screw are code approved for the IBC and IRC for structural strength and corrosion resistance. They are the most popular screws for installing decks.
Given that the shear strength of a 16d common nail is 120 to 150 lbf (depending on the material it is nailed into), it looks like GRK's R4 screws—in any length—are roughly 3x as strong in terms of shear strength, assuming I'm interpreting the table correctly.
The short answer is that, for residential framing, the only situations that call for screws are:
Everything else is usually done with appropriately-sized nails or staples, some of which should be adhesive-coated, ring-shanked, or otherwise special.
I won't endeavor to list all appropriate fasteners and their use-cases here, as that would be an inappropriately broad topic for this site. The most common pneumatic fasteners in my area are ~3" cement-coated framing nails, ~2-3/8" ring-shank nails, and 1-1/2" to 2" cement-coated narrow-crown staples.
Construction adhesive is appropriate for reducing noise and making structures feel more solid, as in staircases. It is not, however, rated for weather resistance scenarios. Mechanical fasteners and building hardware fills that role.