What is difference between classical yoga and the Yoga of Vedic seers?

Answer 1

Contemporary Yoga today as seen in western countries and all over the world only deals with exercises. But exercises fall in only 1 of the 8 steps of yoga known as "Asana". These exercises are good for body and also calms down the mind.
Classical or Contemporary Yoga practice refers to body and mind exercises that give beneficial results when done under proper supervision. There are many qualified instructors for this.

Real Yoga or the goal of Yoga is to achieve the supreme state of being, liberation, enlightenment or svarupavasthiti - whatever term one may choose to descibe it. Yoga noun in sanskrit comes from "yuj" Dhatu (a sort of verb essence). Which means "to unite". The goal of yoga is to make a spiritual union (note the word spiritual and not bodily or physical - please ... ) of an individual's soul to the Supreme soul or the God or the Only Reality.
Thus goal of "Vedic yoga" is to unite an individual with the God and thus "Realization of God" or "Self Realization", "Liberation" etc.
Only an enlightened one or the one who has attained the highest ideal or state of Yoga is considered a proper master to teach this "Vedic" yoga to others. This has been confirmed by all authorities on Yoga of all times. So beware of fake ones with saffron (Orange like) robes, T-shirts with funny Sanskrit hymns and seer like clothes, appearances, behaviors and talks who try to teach you "Yoga". They are neither qualified nor authorized to venture in to the teaching of this subject to others. They can do more harm to you than they can benefit you.

Another one like "Yogi Aurobindo's" Yoga is considered as "Vedic Yoga" among westerners. However it has no basis in Yogic scriptures and authentic Yogic literary resources. It is just an experiment in making. However from what I know of these Aurobindo's follower style Yogis - they are more involved in Power brokerage than yogic practices. Tell me what a true yogi or a sage or a Vedic seer will have to do with brokerage of power ?

Veda is given to us to attain wisdom.
Yoga (Or Vedic Yoga) is a path shown by Vedic Seers to achieve wisdom.
Veda is not meant for your delightment as a poem or a magical phenomenon to entertain you. If you find it so then it is an obstacle in your Yogic path.

Yogic path is scientific. It has no place to cherish funny and entertaining magics that you may find occssionally on Yogic path.
Do not take pride and overly pleasure in something marvellous you come across on Yogic path. Do not chase miracles. Take it sportingly and leave it at that. Control your tendencies of indulgence including entetaing and boosting your ego. Be rational.

Yoga and Veda are one.
But neither are meant for your entertainment or to boost your ego.

Answer 2

Yoga, in Sanskrit means Union. Soul with the supreme. Different sages have provided with different paths. One may choose as per one's own choise, but the end is all the same.