different between attentively vs vigilantly

English

From Middle English attentifly, attentifli, equivalent to attentive +? -ly.

attentively (comparative more attentively, superlative most attentively)

In an attentive manner.
- 1908, Kenneth Grahame, The Wind in the Willows
  `It's a very clean cut,' said the Rat, examining it again attentively.
- When Major saw that they had all made themselves comfortable and were waiting attentively, he cleared his throat and began

vigilant +? -ly

vigilantly (comparative more vigilantly, superlative most vigilantly)

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