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"χαρις" is root of "κεχαριτωμενη", professor. That almost everywhere in the New Testament is translated "grace", unless the topic is favor done by one human to another. Except in Luke 1 where it becomes, curiously, "favor".

The verb used in Luke 1:28

χαριτόω, verb,

Cognate: 5487 xaritóō (from 5486 /xárisma, "grace," see there) – properly, highly-favored because receptive to God's grace. 5487 (xaritóō) is used twice in the NT (Lk 1:28 and Eph 1:6), both times of God extending Himself to freely bestow grace (favor).

Cognate: 5486 xárisma (from "grace," 5485 /xáris) – properly, the operation of grace (divine favor), i.e. a grace-endowment to edify the Church (note the -ma suffix, focusing on the end-result of the endowment of grace).

5486 /xárisma ("grace-gift") divinely empowers a believer to share God's work with others, i.e. Spirit-empowered service to the Church to carry out His plan for His people.

[5486 /xárisma (but not limited to) "spiritual gifts." xarismata (the plural form) literally means "grace-endowments."]

Cognate: 5485 xáris (another feminine noun from xar-, "favor, disposed to, inclined, favorable towards, leaning towards to share benefit") – properly, grace. 5485 (xáris) is preeminently used of the Lord's favor – freely extended to give Himself away to people (because He is "always leaning toward them").

5485 /xáris ("grace") answers directly to the Hebrew (OT) term 2580 /Kaná ("grace, extension-toward"). Both refer to God freely extending Himself (His favor, grace), reaching (inclining) to people because He is disposed to bless (be near) them.

[5485 (xáris) is sometimes rendered "thanks" but the core-idea is "favor, grace" ("extension towards").]

HELPS Word-studies