Not specifically their differences but "~ていました" is used like "USED TO do ~ / WAS doING ~" (for a period of time) while "ました" is just "DID"
E.g. 食べていました = I was eating (maybe describing what I was doing when you called me, for example.)
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E.g. 食べていました = I was eating (maybe describing what I was doing when you called me, for example.)