The OED writes that appraise appeared after praise, and was "for some time, contemporaneously, used in same sense". Further, in the entry for praise they mention:
The late survival of sense 5 probably results from association with appraise v., as though it were an aphetic form of this word.
This mentioned sense is:
To estimate or fix the monetary value of; to fix the price of (something for sale); to appraise.
This meaning of praise--which coincides with appraise's modern meaning--is one of the oldest meanings of the word. Tracing back the historical usages from the OED, the path is something like this:
- 1230: "to express warm approbation of" (transitive)
- 1250: trans. To value, esteem; to attach value to; = prize v.1 2. Obs.
- 1280: trans. To estimate or fix the monetary value of; to fix the price of (something for sale); to appraise. Cf. prize v.1 1. Also intr. Obs. (Eng. regional in later use).
- 1300: In infinitive used predicatively with passive meaning: to be praised; deserving of praise; praiseworthy (now rare)
- 1330: To express approbation; to bestow praise (intransitive)
- 1382: trans. To glorify (a deity, a venerated person, etc.), esp. through ceremony, ritual, song, or prayer; to sing the praises of.
- 1601: trans. To cause (a person or thing) to be praised; to reflect praise or honour on
As you can see, in one of its earliest senses, praise was equivalent to the modern appraise. According to the OED, appraise was first used in 1535. This coincides with the last known uses of praise in this form--marked as 1590 (in reference to the value of something) or 1724 (in reference to a monetary value). I would say that in this time range, the current definition of "appraise" started to shift away from praise. Perhaps once the word appraise was coined, praise was starting to lose the same meaning--thus shifting it from one word to another in order to express the same sentiment.
Finally, the first known use of appraisal to refer to the evaluation of an employee was in 1955.