Are there differences between the activation proteins of Eukaryotes and those of Prokaryotes
In general transcription activators are transcription factors. These are very different in eukaryotes although some families share similar domains (e.g. two component signalization). I recommend you read through these two chapters to get a more complete overview on the differences.

https://www.ncbi.nlm.nih.gov/books/NBK21683/

https://www.ncbi.nlm.nih.gov/books/NBK21572/