These links may help:

https://www.esplanner.com/question/social-security-differs-ssagov-estimate

https://www.esplanner.com/question/incorrect-social-security-benefit-ver...

I've seen results within ~$1/month comparing ESPlanner estimates and SS actual benefits.

Best,
Brian

Here's our FAQ from Maximize My Social Security which uses the same Social Security code as ESPlanner.

Why can't I get Maximize My Social Security's estimates to match the AnyPIA estimates if I'm under age 62?
Maximize My Social Security (MMSS) assumes the real wage growth from the Trustee's report, which we combine with your inflation rate assumption to calculate future nominal average wages.

The closest, but not exactly the same, AnyPIA assumptions are for no benefit increase beginning with the 2014 increase and the 2013 Trustee's Report Alternative II average wage increase. These assumptions use the same real wage growth from the Trustee's report, but combine it with the Trustee's estimated future inflation rates to calculate future nominal average wages and they cause the PIA to be reported in real 2015 dollars.

Because MMSS and AnyPIA use different inflation assumptions they estimate different future nominal average wages, which means that the indexed earnings differ, which, in turn, means the PIAs will also differ.
Changing the inflation rate and nominal rate of return in MMSS does not affect the real wage growth since it comes from the Trustee's report.

So, it's the constant future inflation assumed by MMSS/ESPlanner or the variable future inflation assumed by Social Security Trustees.

Take your pick.