There really isn’t an industry standard to say what “ER” and “LR” entails, it’s more of a branding exercise than anything else.
For example, the A321 NEO LR is just an MTOW increase with increased fuel capacity over the regular variant. The ER variants of the Boeing 767-200/300 and 777-200 also use this strategy to claim improved range as an “ER” variant but Airbus prefers the “LR” moniker.
Airbus’ A350-900 uses another name for its long-range variant, they call it the “ULR” even though it uses the same strategy as the A321 NEO LR to improve its range.
The 777-200LR and 777-300ER both feature identical structural improvements, more powerful engines, revised winglets, increased fuel capacity, and improved MTOW compared to its regular variants. This is more of an overhaul compared to its peers, but use different naming conventions.
Embraer calls their models with added range an “IGW” which stands for “Improved Gross Weight”.
Are you confused yet? Good, because there is no method to this madness. ;)