With respect, you've made several incorrect statements and assumptions ...
To begin with, the buttress thread form is NOT made up to the base of the triangle, it's made to to a point between the base and the apex. This may seem a minor difference, but it's critical to achieving proper interference fit between the coupling and pin which, among other issues, is critical to ensuring proper leak resistence and tensile capacity.
Additionally, within a given casing OD size, the API buttress thread form is identical, regardless of weight or grade (though from memory, small diameter casing in the 4½ range may have several thread forms). Thus, relative to the question Boas asked, all 16" BTC connections are fully interchangeable with all 16" casing weights, or going slightly larger, all 20" BTC connections with all 20" BTC weights (see API Spec 5B).
If 18⅝" was offered in more than one weight, then they would all be interchangeable.
Further, conductor, i.e. line pipe, is not manufactured according to standard and limited ODs and weights as casing and tubing are. In brief, a casing buyer specifies OD and casing weights according to a relatively short list in each API-recognised diameter.
Without digressing, end-users may order non-standard casing and tubing sizes in any dimension they wish, but the API-recognised sizes and weights are relatively limited.
Relative to Boas' question, with API casing, the ONLY weight available in 18⅝" is 87# with it's 0.435 wall thickness (API Spec 5CT, Table E1).
By comparison, a line pipe buyer specifies OD and wall thickness according to their requirements.
Again, relative to the question asked by Boas, line pipe OD and wall thickness may be ANY increment in either OD or thickness between 18" and 22" OD and 0.281" and 1.771" wall thickness (API Spec 5L, Table 9).
The issue, as I stated and Augusto amplified on, is the geometry of the finished product. With 18⅝" casing, this is relatively simple because there is only one acceptable set of ranges; those for 18⅝" 87#.
With 18⅝" conductor, what has to be verified is whether or not the buyer actually specified (and the manufactured achieved) a product that would be dimensionally identical to 18⅝" x 87# casing.
I could have recommended that Boas review a relatively large dataset, however chose to recommend that he simply confirm the connections' finished geometry was / is identical for the reasons above.
The pitch diameter will confirm the 'z axis' of the two products (casing v conductor) connections is the same, and the thread form, thread height, taper, and lead will confirm the proper fit when made up.
If they are both BTC, there should be no issue of connecting them..
The short answer is that they likely are.
The longer answer is that conductor and casing are not typically manufactured using the same processes, so interchangeability needs to be verified via thread inspection. The TI should include thread form, thread height, taper, lead, and stand-off (the latter may be measured using a Pitch Diameter gauge, or ring and plug gauges).
Any competent machine shop that cuts or repairs connections must have those gauges (though maybe not 18⅝" ring and plug gauges but the PD gauge is perfectly acceptable). The inspection should require no more than an hour or so from start to finish.