Do these phrases convey the same meaning? Is an informed guess by definition, also, an educated guess?
which are all listed as (potential) synonyms for approximation.
Differences: (emphasized, in every day use these are very subtle if present at all)
Educated guess, presumes established competency (formal or informal) in the field in which the guess is made.
Informed guess, I think, is typically used when the one who is making a guess got informed through a specific action. For example in such cases as after briefing, examination, interrogation or an interview.
Often the distinction is not made, because it can be said that in an ordinary context one can not be educated without being informed and vice versa.
I would treat these terms as synonymous. Both "informed" and "educated" work to establish the speaker as having some kind of privileged knowledge rendering the guess in question as being more reliable than not.
We could, I suppose, try to parse the difference between the two qualifiers as having some slight nuance but that would be pushing the envelope.
An "educated guess" is a guess, but one that is based on circumstantial evidence. E.g. he notes that you are sporty, so an "educated guess" would be you liked soccer. That may not be true, you may like "sprinting", but the guess is based on circumstantial evidence.
An "informed guess" is a synonym of "educated guess".