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