There are some Vedic texts which are similar to (or same as) those of Avesta (just like some Sikhism scriptures also do have references to Vedic stories, Vedic names like Prahlad, Hari etc.). For example:

• yad antarikshe yadi vata asa yadi vriksheshu yadi volapeshu yad ashravan pashava udyamanam tad brahmanam punar asman upaitu (Atharva Veda 7:66)^[7]
• yadi antareekshe yadi vaate aasa yadi vriksheshu yadi bolapashu yad ashravan pashava ud-yamaanam tad braahmanam punar asmaan upaitu (Zend Avesta Prishni, Chapter 8, Gatha 12)

Has the same translation to English:

• O Lord! Whether you be in the sky or in the wind, in the forest or in the waves. No matter where you are, come to us once. All living beings restlessly await the sound of your footsteps.^[8]

Another example:

• mahaantaa mitraa varunaa samraajaa devaav asuraaha sakhe sakhaayaam ajaro jarimne agne martyaan amartyas tvam nah (Rigveda: 10:87:21. Translation: O Supreme Being, you are fire, you are the sun, you are water. You have appeared to us as Father, as our ruler, as our friend and as our teacher. O Great Father, you are beyond aging but we are not. You are beyond death but we are not. In spite of that you have given us the great fortune to call you our friend.)
• mahaantaa mitraa varunaa devaav ahuraaha sakhe ya fedroi vidaat patyaye caa vaastrevyo at caa khatratave ashaauno ashavavyo (Gatha 17:4 Yashna 53:4. Translation: Translation: O Ahura Mazda, you appear as the father, the ruler, the friend, the worker and as knowledge. It is your immense mercy that has given a mortal the fortune to stay at your feet.)

Monism in Zend Avesta and Vedas:

• Veda: majadaah sakritva smarishthah (Only that supreme being is worthy of worship.)
• Zend-Avesta: madaatta sakhaare marharinto (Gatha 17:4 Yashna 29. Only Ahura Mazda is worthy of worship.)

Also:

• kasmai devaaya vidhema (From Atharva Veda)
• kamhai devaaya vidhema (From Zend Avesta)

Both mean “to which God should I sacrifice?”^[9] Vedas also have some reference to ancient Persia. In Sanskrit its name is Paarasya, and Zoroastrian name was Paarada. Manu Samhita the following quote on the subject:shanakaistu kriyaalopaadimaah kshatriyajaatayoh vrishalatvam gataaloke braahmanaadarshanena ca poundrkaashcodradaavidaah kambojaah yanaashokaah paaradaa pahlavaarshceenaah kiraataah daradaakhashaah (On breaking down of the family and other social structures, a section of kshatriyas came to be called as shoodra at first and yavana later. The inhabitants of Persia belong to that group.) Four varnas (castes) in Avestan and Sanskrit:

• atharva (the priest, vedic Brahmana)
• ratheshtan (the warrior, rath means ‘chariot’ in Sanskrit - kshatriyas)
• vastriyoksiya (the agricultural labourer, vaishyas)
• huits (the labour class, shudras).

• Who were the Aryans?

  Aryans of the Avesta and Rig Veda

  The Indo-Iranian group whose members composed the Zoroastrian scriptures, the Avesta, and the Hindu scriptures, the Rig Veda, called themselves Aryans (Airya/Airyan in the Avesta and Arya/Aryan in the Vedas).
  
  The Rig Veda is the older portion of the Vedas. The Avesta and Rig Veda are the only known ancient texts that contain references to Aryans.
  
  The next contemporaneous references are in the inscriptions of the Achaemenian Persians (see Achaemenian History as well as our page on Naqsh-e Rustam), and classical Greek texts such as those of Herodotus and Strabo, where the the references are exclusively regarding the Medes' and Persians' ancestry and their Central Asian connections.