Difference between Yoga philosophy and Vedanta

In a nutshell, both yoga philosophy and Vedanta accept the Vedas as Pramāṇa (प्रमाण) or an authoritative source of knowledge. They are, thus, two of the six āstika darśanas (those that accept Vedic authority)

Yoga philosophy is considered a sister philosophy of Sānkhya and derives most of the material from Sānkhya with the most notable exception in similarities being that Yoga includes Ishwara (God) as an anchor to still the mind, whereas Sankhya, in its purest form, called Nirishwara Sankhya, has no mention of Ishwara. Yoga philosophy was chronologically developed before Vedanta and it was codified into sutras called Yoga Sutras, much later (thought to be ~400 BCE), by a great Rishi named Patanjali. 

Vedanta, on the other hand, is derived from the final portion of the Vedas also called the Upanishads. This is how the term Veda +antah (end) = Vedanta was coined to reflect the material being derived from the final portion of the Vedas. Vedanta or the final portion of the Vedas contain the material about the nature of our true self, called Ātma. 

Vedanta was codified into sutras known as Brahma Sutras by the great Rishi Veda Vyasa himself. Though the date is not clear and traditional scholars put it somewhere around 3000 BCE, based on the beginning of the Kali Yuga, while historians put it at a much more recent date of between 400BCE and 200 BCE . 

Vedanta, considered the most recent of the Ṣaḍ-darśanas (six viewpoints or philosophies), freely borrows from all the prior five philosophies and is said to supersede all the five and is said to have the most holistic and accurate interpretation of the Vedas. Thus Yoga philosophy can be thought as a subset of Vedanta (Ref. 1). Vedanta accepts all the practices of yoga to still the mind and attain the state of "Chitta-Vritti-Nirodah" (State of cessation of the mental fluctuations) but Vedanta (Advaita Vedanta) rejects the dual philosphy of Yoga in terms of the Universe being comprised of Purusha and Prakriti. Vedanta also rejects the notion of multiple Purushas that is found in Yoga and Sankhya.

The following table does a comparison of the two:

References:

1) Swami Sarvapriyananda's video "The path beyond Yoga and Vedanta"