There is very little difference between a solicitor and a notary public signing a document. They perform the same function, checking documents, adding a certification and signing the document.
In general, a solicitor can certify 99% of documents. This is widely accepted for use in the UK and overseas. However, there are some documents that specifically state ‘witnessed by a notary public’. In addition, a few authorities or countries may only accept certification by a notary public. However, this is unusual and solicitor certification is normally accepted without question.
If the person asking for your document specifically requests you use a notary public, then it is safer to use a notary to avoid a document being rejected.
