Generally, if your document is going to be used in the UK it will require a Commissioner for Oaths certification. If it is going to be used abroad, it will require notarisation. What is the actual difference (apart from the price)? Simply put, certification will receive a stamp and notarisation with receive a stamp and a red seal. Both documents will be signed by myself, but under two different capacities.
BUT my document says it can be signed by my accountant/solicitor? This suggests your document can be used in the UK, as solicitors and accountants can certify documents for this purpose.
A notary can also do the same. The only difference is an accountant/solicitor is a Commissioner OF Oaths and a notary is a Commissioner FOR Oaths. What difference does this make to you? Absolutely none. My only advice would be double check with the people receiving your document what type of certification is required. It could end up saving you quite a bit of money.