Φέτος comes from the ancient greek εφέτος, from ἐπ’ ἔτος, meaning the current year. Χρόνος and έτος are interchangeable in cases like
He is 9 years old - Αυτός είναι 9 χρονών/ετών
He died 9 years ago - Αυτός πέθανε πριν 9 χρόνια/έτη
I'll be back in two years - Θα γυρίσω σε δύο χρόνια/έτη
The new year - Ο νέος χρόνος/το νέο έτος
BUT, έτος means only year . Χρόνος also means time. So they are not interchangeable in cases like
I need time to think - (Εγώ) Χρειάζομαι χρόνο για να σκεφτώ
I would like to spend more time with my family - Θα ήθελα να περνάω περισσότερο χρόνο με την οικογένεια μου
Hope this is clear enough ^.^
φέτος specifically refers to "(during) the year in which are right now".
For example, in sentences such as "I earn more money this year than I did last year" or "This year, I want to travel to Greece on holiday" or "He has not visited me yet this year."
I believe φέτος is the adverb "this year" meaning "during this year" and αυτός ο χρόνος would just be the noun "the year that is happening now".
So you might say Αυτός ο χρόνος είναι πολύ ιδιαίτερος "This year is very special" ("this year" as subject) but not (I think) Θα πάω στην Ισπανία αυτόν το χρόνο "I will go to Spain [during] this year" ("this year" as adverbial of time).