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Vine's Expository Dictionary of NT Words [1]

1: Ἄλλος (Strong'S #243 — Adjective — allos — al'-los )

is used, in its neuter form, allo, in  Galatians 5:10 , lit., "another thing," with the meaning "otherwise." See Other , No. 1.

2: Ἄλλως (Strong'S #247 — Adverb — allos — al'-loce )

the adverb corresponding to No. 1, is translated "otherwise" in  1—Timothy 5:25; the contrast is not with works that are not good (No. 3 would signify that), but with good works which are not evident.

3: Ἑτέρως (Strong'S #2088 — Adverb — heteros — het-er'-oce )

is used in  Philippians 3:15 , "otherwise (minded)," i.e., "differently minded." Contrast No. 2, and for the corresponding difference between the adjectives allos and heteros, see Another.

4: Ἐπεί (Strong'S #1893 — Conjunction — epei — ep-i' )

when used of time, means "since" or "when;" used of cause, it means "since, because;" used elliptically it means "otherwise" or "else;" "otherwise" in  Romans 11:6 (the 2nd part of the ver. is absent from the most authentic mss.);   Romans 11:22; in  Hebrews 9:17 , AV, "otherwise (it is of no strength at all)," RV, "for (doth it ever avail?)." See Else.

 Matthew 6:1 Luke 5:36  2—Corinthians 11:16Teach.

King James Dictionary [2]

OTH'ERWISE, adv. other and wise, manner.

1. In a different manner.

Thy father was a worthy prince, and merited, alas! a better fate but heaven thought otherwise.

2. By other causes.

Sir John Norris failed in the attempt of Lisborn, and returned with the loss, by sickness and otherwise, of 8000 men.

3. In other respects.

It is said truly, that the best men otherwise, are not always the best in regard to society.

Webster's Dictionary [3]

(1): ( adv.) In different circumstances; under other conditions; as, I am engaged, otherwise I would accept.

(2): ( adv.) In a different manner; in another way, or in other ways; differently; contrarily.

(3): ( adv.) In other respects.