No they are not the same. First of all, correcting entries are posted to correct errors. If a wrong entry was posted, the correcting entry is posted to fix that.
The adjusting entries are not correcting entries. The adjusting entries are posted at the year end to adjust for things like accruals and prepayments. For example, at the year end, a company will have to post entries to accrue for expenses that are not yet invoices or for revenue received but not yet earned.
All these entries are called adjusting entries.