Actually both these scores are telling you the same thing. They can both be interpreted as Very Good Results, and any finer level of detail is chasing noise. Some minimal google scholar searching suggests that WAIS correlates with itself somewhere between .7 and .9, and that a correlation of .8 across different kinds of test is considered 'very good'. This means discrepancies of the size you describe are not super rare. There's another factor working against you too, because you're in the tail of the distribution, and those agreement numbers are overall! The test-retest consistency inevitably gets worse as you get out into the tails.
There's a nice longer discussion here:
"...population averages of thousands of IQ estimates [are] valuable and useful research tools. It just means you shouldn’t use it on yourself."
"...even if you avoid the problems mentioned above and measure IQ 100% correctly, it’s just not that usefully predictive."
"After investing so much work debunking IQ denialists, I feel like this is really – I don’t know – diluting the brand. But I actually think it’s not as contradictory as it looks... If you really understand the idea of a statistical predictor"