Translating is not an exact science and there isn't always a one-to-one mapping between words in Esperanto and words in English. The translations you have found will just be the interpretation by one person and don't necessarily represent an official definition. Probably the closest thing we can get to an official definition in Esperanto would be the one in PIV which is available for free online at vortaro.net.
There the definitions are:
Laboristo Homo, kiu sin dungigas por laboro
Laboranto Homo, kiu laboradas
And labori is:
Uzi siajn korpajn aŭ mensajn fortojn, por produkti aĵon, plenumi taskon, atingi efikon
So perhaps with that definition a laboranto is just someone who does some work, which for example could be to look after their own garden and they aren't necessarily paid. Whereas a laboristo is specifically dungita, meaning they are paid.
I think this more or less matches a regular interpretation of the suffixes -ant and -ist. -ist implies that the individual is a professional in some respects and -ant just means that the person generally does the action.
This would be the same for parolanto and parolisto. The former could be used to describe a person giving a talk during a conference. It might be their first talk and they don't do it professionally, whereas calling them a parolisto would imply they do it often and probably get paid for it.