You are referring to two of the three types of samadhi, which is a term for the highest levels of consciousness. Eastern mystics have categorized these high levels of consciousness, which always involve direct apprehension of the Divine Source Energy of the Universe. They are:
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• Nirvikalpa samadhi
• Savilkalpa samadhi
• Sahaja samadhi

Nirvikalpa Samadhi
In nirvikalpa samadhi, you are the giant heart of the Universe. Even the Universe is tiny within the vastness of your being. It is a state of unlimited bliss and peaceful joy.

Nirvikalpa samadhi is considered to be the highest samadhi that most Spiritual Masters can attain. But it only lasts a few hours or days at most. Then it’s time to come back into the world of the physical. Often, we don’t want to come back into the world again. It is even said that if we stay there for 18–21 days, our soul may leave the body and cross over to the Other Side.

I have read of Spiritual Masters who have gone into Nirvikalpa samadhi and announced to their students, “Today is a good day to die.” They realized that they had attained their highest samadhi. Now it was not possible for them to keep carrying on in the physical plane.

This samadhi is not a survival state. It is a pervasive ecstasy. We really cannot carry on with material life in the world while in Nirvikalpa.
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Savikalpa Samadhi
In Savikalpa samadhi, which also only lasts for a period of time, we lose all consciousness of time and space. As there is no time, there is nothing to get done, there is nothing to do. It is already all done.

In this state of samadhi we see ourselves merely as an instrument to channel the purpose of the Divine. We do not need to do anything, it is already perfect and complete. There is nothing to accomplish, nothing to attain, nothing to do.

Unlike in Nirvikalpa samadhi where all thought has stopped, in Savikalpa samadhi thoughts arise, but they do not affect you. You just notice them without getting involved in them.

Sahaja Samadhi
Sahaja samadhi is the state of higher consciousness in which we are capable of working in the physical plane, while still maintaining Nirvikalpa samadhi. It’s simultaneously one foot in heaven and one foot on earth.

In Sahaja samadhi we do the daily tasks and chores. But each of these activities is infused with the bliss that only present moment awareness of the Divine can bring.

It is said that few Spiritual Masters have achieved Sahaja samadhi. It comes through grace. Grace is a deep spiritual topic of it own. It is a gift of insight from the divine and cannot be forced.

Twin flames are eternally united, though they may not meet physically during every lifetime. This is what qualifies them as twin flames. They are essentially the same person in two different bodies. Therefore, there can be no separation, ever.

They may live in different parts of the world. Or maybe they will choose alternating lifetimes to appear in the Physical plane. But they can never be separated in the world of the Spirit. Perhaps they will meet during a lifetime. When they do, they know it instantly.

Twin flames are not the same as soul mates. Soul mates meet in a lifetime to complete something that was left undone in a past life. They always meet for the purpose of spiritual expansion and growth, or to complete a learning experience, or to complete the circle of love.

I have seen this in families, where there is a deep soul connection between a mother or a father and certain children. These children have recirculated into their parents’ lives. In some cases the love is so deep, they re-emerge to experience it once again, but in a new way.

Karmic Counterparts can meet to complete a relationship that was not resolved in a previous existence. Sometimes these kinds of soul mate relationships are difficult but very rewarding. They are two distinct souls living in the Super-Soul of the cosmos. Yet they are eternally connected and may re-emerge in different lifetimes together.

Twin flames are soul mates AND the same person (yet split into two bodies, like cosmic twins). Both Soul Mates and twin flames have this in common: It is a spiritual union, and as such, it is eternal. So there is never any permanent separation. It is a bond based in infinity.