The words τεθεμελιωμένος (θεμελιόω) and ἑδραῖος have similar meanings. They both occur in Colossians 1:23; "grounded (τε) and settled (ἑδ)," or "founded and firm." τεθεμελιωμένος (from θεμέλιος, 'a foundation') suggests the idea of being 'secured to the foundation:' thus in Matthew 7:25; Luke 6:48 , it is "founded on a rock." In Hebrews 1:10 the Lord "founded the earth;" Ephesians 3:17 , "rooted and founded in love;" and 1 Peter 5:10 , "make you perfect, strengthen, 'found' you."
ἑδραῖος (from ἕδρα 'a seat or sitting') has more the thought of being 'stable, firm, within.' Besides Colossians 1:23 it occurs only in 1 Corinthians 7:37 , "he that stands firm in his heart;" and in 1 Corinthians 15:58 , "my beloved brethren, be ye firm."