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Genuinedealz has wire specs posted here:

BESTBOATWIRE UL 1426 Marine Wire Specifications



From that chart the OD is .330 inches and the insulation thickness is .060. I suspect the OD is with insulation. that gives:

.330-.120 = .210

That .210 spec is pretty close to the 6 AWG lugs you got.

The .15/.16 measurement you got seems more like 8 gauge. From the same document for 8 AWG:

.270-(2* 0.045) = .180


The wire size should be clearly labeled on the insulation. Did you double check to make sure they didn't send you the wrong gauge (8?) by mistake?

Conductor properties for building wire is covered in Table 8 of the NEC.

enblethen wrote:
You need to look under the correct type of wire. SAE multi strand and marine wire is smaller diameter then building style wire either stranded or solid.
If you look at the NEC building wire is only seven strand for stranded. It is .061 inches in diameter.
Here is listing for automotive SAE wire and MarineSAE wire sizes
I normally drop one connector size for SAE automotive and marine wire.

Supposedly the vendor I used sells high quality AWG cable. So I looked at that table, and taking their overall 6 AWG OD, less 2x the insulation, I get .212. Big difference from what I got. Hmmmm.

You need to look under the correct type of wire. SAE multi strand and marine wire is smaller diameter then building style wire either stranded or solid.
If you look at the NEC building wire is only seven strand for stranded. It is .061 inches in diameter.
Here is listing for automotive SAE wire and MarineSAE wire sizes
I normally drop one connector size for SAE automotive and marine wire.