No scans necessary for this one.
To qualify as a reprint, it must qualify the following criteria:
1. It has the same name as the previous print. PCL has deliberately used this rule when making cards like Old Amber Aerodactyl to prevent players from using Old Amber.
If the cards don't have the same name, it is not a reprint, end of story. This is your first check when asking what a reprint is, so don't bother with the effect text until you have confirmed the cards have the same name.
2a. If the card in question is a Pokemon,
everything must be the same in order to qualify as a reprint. Changing even a single thing disqualifies it from being allowed under the reprint rule. The best example of this is Sneasel from Neo Genesis and Undaunted:
On the left is the original print. On the right is the "reprint." Everything is the same until you hit the bottom stats. The new Sneasel has a Weakness and a reduced Resistance. That's enough to make them two different cards, so the original print would not be allowed under the reprint rule. Notice that the wording for Beat Up has been updated even though it functions in the same way.
2b. If the card in question is a Trainer, it can be used, but the wording of the most recent card supersedes the wording of the old one. Sometimes the wording between two prints varies significantly or the cards have two different effects entirely. In those cases I'm not sure if you need a reference or you just can't use them but I don't believe any cards like that are present in Standard.
Applying these to your questions:
There is no card called Professor Oak allowed in Standard or Expanded, so it's not legal. Remember that if the names aren't the same, they aren't reprints, even if the effect is the same as an existing card.
There is also no card called Professor Elm, so it's not allowed, either.
Sycamore and Juniper are special cases where you are not allowed to include them both in the same deck. This is not because they are reprints of each other, but because it's a very powerful Supporter which would unbalance the game if you could have four of each in your deck.
