Might be easier if you post details of an example transaction.
In general...
If you receive free shares/RSUs then the full market value at the time that you take ownership of them is assessable for income tax/PRSI/USC.
If you receive the shares at a price that's at a discount to the full market value then the discount is assessable for income tax/PRSI/USC.
In many (most?) cases these days this is dealt with via payroll.
If, after taking ownership of the shares/RSUs, you hold onto them and sell them at a later date then any gain/loss is dealt with under the self-assessed CGT system. E.g. a gain (less your annual personal allowance of €1,270 if not previously used up and less any previously incurred capital gains) is subject to 33% CGT.