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isn't the first jhanas all about concentration?

It is about vitakka and vicāra. This also concentrates the mind by cutting out distractions as you continuously return to your anchor object. To put it in another way it is developing vitakka & vicāra which also results in concentration.

abandonment by suppression

This is a kind of suppression. You periodically bring you mind to the object of concentration thereby not letting other thoughts that arise.

The above description looks more like abandoning Nivarana. [Nīvarana,pahana Vagga] To get into Jhana you have to abandon the hindrances but abandoning hindrances alone will not get you into Jhana. To get into the 1st Jhana what you need is vitakka & vicāra while abandoning the Hindrances also. Also Jhana is a means to abandon the hindrances. Being without hindrances in the absence of vitakka & vicāra, I think, does not always result in Jhana as this is one of the factors in the 1st Jhana. For more on this see The Five Mental Hindrances and Their Conquest Selected Texts from the Pali Canon and the Commentaries compiled and translated by Nyanaponika Thera.

Put it in another way concentration and abandonment are side benefits of developing the Jhana through vitakka & vicāra.

isn't the first jhanas all about concentration?

It is about vitakka and vicāra. This also concentrates the mind by cutting out distractions as you continuously return to your anchor object. To put it in another way it is developing vitakka & vicāra which also results in concentration.

abandonment by suppression

This is a kind of suppression. You periodically bring you mind to the object of concentration thereby not letting other thoughts that arise.

The above description looks more like abandoning Nivarana. [Nīvarana,pahana Vagga] To get into Jhana you have to abandon the hindrances but abandoning hindrances alone will not get you into Jhana. To get into the 1st Jhana what you need is vitakka & vicāra while abandoning the Hindrances also. Also Jhana is a means to abandon the hindrances. Being without hindrances in the absence of vitakka & vicāra, I think, does not always result in Jhana as this is one of the factors in the 1st Jhana. For more on this see The Five Mental Hindrances and Their Conquest Selected Texts from the Pali Canon and the Commentaries compiled and translated by Nyanaponika Thera.

Put it in another way concentration and abandonment are side benefits of developing the Jhana through vitakka & vicāra.

isn't the first jhanas all about concentration?

It is about vitakka and vicāra. This also concentrates the mind by cutting out distractions. To put it in another way it is developing vitakka & vicāra which also results in concentration.

abandonment by suppression

This is a kind of suppression. You periodically bring you mind to the object of concentration thereby not letting other thoughts that arise.

The above description looks more like abandoning Nivarana. [Nīvarana,pahana Vagga] To get into Jhana you have to abandon the hindrances but abandoning hindrances alone will not get you into Jhana. To get into the 1st Jhana what you need is vitakka & vicāra while abandoning the Hindrances also. Also Jhana is a means to abandon the hindrances. Being without hindrances in the absence of vitakka & vicāra, I think, does not always result in Jhana as this is one of the factors in the 1st Jhana. For more on this see The Five Mental Hindrances and Their Conquest Selected Texts from the Pali Canon and the Commentaries compiled and translated by Nyanaponika Thera.

isn't the first jhanas all about concentration?

It is about vitakka and vicāra. This also concentrates the mind by cutting out distractions as you continuously return to your anchor object. To put it in another way it is developing vitakka & vicāra which also results in concentration.

abandonment by suppression

This is a kind of suppression. You periodically bring you mind to the object of concentration thereby not letting other thoughts that arise.

The above description looks more like abandoning Nivarana. [Nīvarana,pahana Vagga] To get into Jhana you have to abandon the hindrances but abandoning hindrances alone will not get you into Jhana. To get into the 1st Jhana what you need is vitakka & vicāra while abandoning the Hindrances also. Also Jhana is a means to abandon the hindrances. Being without hindrances in the absence of vitakka & vicāra, I think, does not always result in Jhana as this is one of the factors in the 1st Jhana. For more on this see The Five Mental Hindrances and Their Conquest Selected Texts from the Pali Canon and the Commentaries compiled and translated by Nyanaponika Thera.

Put it in another way concentration and abandonment are side benefits of developing the Jhana through vitakka & vicāra.

isn't the first jhanas all about concentration?

It is about vitakka and vicāra. This also concentrates the mind by cutting out distractions. To put it in another way it is developing vitakka & vicāra which also results in concentration.

abandonment by suppression

This is a kind of suppression. You periodically bring you mind to the object of concentration thereby not letting other thoughts arise.

The above description looks more like abandoning Nivarana. [Nīvarana,pahana Vagga] To get into Jhana you have to abandon the hindrances but abandoning hindrances alone will not get you into Jhana. To get into the 1st Jhana what you need is vitakka & vicāra while abandoning the Hindrances also. Also Jhana is a means to abandon the hindrances. Being without hindrances in the absence of vitakka & vicāra, I think, does not always result in Jhana as this is one of the factors in the 1st Jhana. For more on this see The Five Mental Hindrances and Their Conquest Selected Texts from the Pali Canon and the Commentaries compiled and translated by Nyanaponika Thera.

isn't the first jhanas all about concentration?

It is about vitakka and vicāra. This also concentrates the mind by cutting out distractions. To put it in another way it is developing vitakka & vicāra which also results in concentration.

abandonment by suppression

This is a kind of suppression. You periodically bring you mind to the object of concentration thereby not letting other thoughts that arise.

The above description looks more like abandoning Nivarana. [Nīvarana,pahana Vagga] To get into Jhana you have to abandon the hindrances but abandoning hindrances alone will not get you into Jhana. To get into the 1st Jhana what you need is vitakka & vicāra while abandoning the Hindrances also. Also Jhana is a means to abandon the hindrances. Being without hindrances in the absence of vitakka & vicāra, I think, does not always result in Jhana as this is one of the factors in the 1st Jhana. For more on this see The Five Mental Hindrances and Their Conquest Selected Texts from the Pali Canon and the Commentaries compiled and translated by Nyanaponika Thera.