"A mushroom and a tomato."
Is פטרייה also spelled as פטריה ? Is there any difference between these two forms?
Both forms are correct. פטריה is the original form, but along the years the spelling of many words have change to make them easier to read without Nikkud. One of the changes is using double י to mark that the י here is a consonants and not a vowel (it should sound like 'Y' instead of 'I')
I'd like to modify that a bit. You don't need to write a double י when it's a consonant. The best practice is to add a second י when there are both an "i" vowel sound and a consonant "y", as in the case of פטרייה and עגבנייה.