Detecting which words are the same between two pieces of text
Since you do not show any work of your own, I'll just give an overall algorithm.
First, split each text into its words. This can be done in several ways. You could remove any punctuation then split on spaces. You need to decide if an apostrophe as in dog's is part of the word--you probably want to leave apostrophes in. But remove periods, commas, and so forth.
Second, place the words for each text into a set.
Third, use the built-in set operations to find which words are in both sets.
This will answer your actual question. If you want a different question that involves the counts or positions of the words, you should make that clear.
I need some python advice to implement an algorithm.
What I need is to detect which words from text 1 are in text 2:

Text 1: "Mary had a dog. The dog's name was Ethan. He used to run down
  the meadow, enjoying the flower's scent."
Text 2: "Mary had a cat. The cat's name was Coco. He used to run down
  the street, enjoying the blue sky."

I'm thinking I could use some pandas datatype to check repetitions, but I'm not sure.
Any ideas on how to implement this would be very helpful. Thank you very much in advance.