'Regarding' and 'with regard to' - note the 'to' - can be used in the same way. You can say either 'regarding your recent application for the post of junior manager' or 'with regard to your recent application for the post of junior manager', and the meaning will be the same. By the way, please don't make the mistake - common amongst native speakers - of trying to use 'regards' in this context. The correct expression is 'with regard to', not 'regards'. 'Regards' are good wishes, as in 'Give my regards to your family'. This word is not an alternative to 'regard'.

I don't think that exist a difference it all. Means the same I think only the formal use. . But I'm not sure. .