In the past, perhaps even on this site, we have shown the distinct definitions of these words. Of course, modern bibles simply drop stablish and use establish all over. Modern dictionaries are, likewise and predictably, no help. In short, we framed ‘Establish’ with synonyms such as initiate, founded, begin. We often see businesses, churches, even families, that had been established at such and such a date in history. The Apostle Paul will make a reference to his “entrance in unto you”— recounting their initial meeting (Thessalonians).
Contrariwise, ‘Stablish' refers not to a foundation, nor an initial start or entrance; but rather it refers to building, strengthening, growing, edifying, and increasing.
Here is an example of these two words at work:
“ …And sent Timotheus…to establish you, and to comfort you concerning the your faith…” (1 Thess. 3:2)
Paul had only been with the Thessalonians for 3 sabbaths (less than a month) before he and his company got run out of town by envious Jews. Now he was concerned about these new believers and sent Timothy to check on them: to know their faith, to see if they were grounded, if they had a firm foundation. In short, were they established?
Timothy visits the Thessalonians, and then returns to Paul with a very encouraging and positive report of their faith (1 Thess. 3:6-8). Paul expresses his joy for their testimony and then he states his prayer for their perfection, their maturity—that they would increase and abound. What one word does he use to summarize his desire for them, now that they are both grounded and growing?
“…To the end he may stablish your hearts unblameable…” (v. 13).
It would be a mistake, a dulling down, to replace the ‘stablish’ of v.13, with ‘establish.’ As it is written, it fits the flow, the running narrative of Paul’s epistle. Each word supports, and is supported by, the synonyms of their own context; revealing Paul’s desire from initial establishing, to a mature edifying: stablishing.