Apostille requirements in Thailand

I note that for some non-visa processes, the Thai authorities require the certification (i.e. Apostille) of documents - paying the local embassy to put a stamp on so that it will be processed.

Can this be done outside of Thailand in the home country? It seems unnecessary to cart lots of originals of various things around with you all over the place.

What's the difference between the following services in terms of the "output"?
How to Apply
Apostille and Legalisation in Thailand | London Notary | Public Notary London