In the Anapanasati Sutta, what is the difference between mind and mental processes?

Gil Fronsdal explains the difference between mental fabrications/processes (Tetrad II) and the mind (Tetrad III) by describing Tetrad II a bit differently:

1. Pay attention to the enjoyment or rapture;

2. As time passes pay attention to the more refined pleasure that appears;

3. Experience or be sensitive to our tight thinking;

4. Relax the strained thinking that interrupts the meditation.

and Tetrad III

1. As your strained thinking starts subsiding, notice the quality of the mind.

2. Gladden the mind if the state of mind is down.

3. Steady the mind if it is too excited.

4. Release the deep preoccupations of the mind by looking at the drawbacks of the stress. Notice how small our problems are compared to the hugeness of the universe and time. Be creative and use what contemplation works with trial and error. Just like in the sutta, we must put aside greed and distress in reference to the world. The outside world that the preoccupations are aimed at.

Tai Sheridan in 'Buddha in Blue Jeans' seems to warning against mental fabrications in the practice of Buddhist Meditation in this short section from his book:

'Sit anywhere and be quiet:

on a couch, a bed, a bench, inside, outside,

leaning against a tree, by a lake, at the ocean,

in a garden, on an airplane, in your office chair,

on the floor, in your car.

Meditation cushions are okay too.

Sit at any time: morning, night,

one minute, three years.

Wear what you've got on.

Loosen your waist so that

your belly can move with your breath.

Sit as relaxed as possible.

Relax your muscles

when starting and during sitting.

Sit with your back straight but not stiff.

Keep your head upright with your ears level.

Respect all medical conditions.

Only take a posture you can.

All postures are okay.

Do what you can do.

Keep your eyes slightly opened and out of focus.

Closing them will make you sleepy and sometimes busy.

Opening them wide will keep you busy.

Breathe naturally through your nose.

Enjoy breathing.

Feel your breath.

Watch your breath.

Become your breath.

Be like a cat purring.

Follow your breath like ocean waves

coming in and out.

When you get distracted,

come back to the simplest

and most basic experience

of being alive,

your breathing.

That's it.

No belief.

No program.

No dogma.

You do not have to be Buddhist.

You can be of any faith, religion,

race, nationality, gender,

relationship status, or capacity.

Just sit quietly,

connect with your breath,

and pay attention

to what happens.

You will learn things.

Do it when you want.

You decide how much is enough for you.

If you do it daily, it will get into your bones.

Please enjoy sitting quietly!

The only way to learn sitting quietly is to do it.'

The second tetrad includes the term "citta sankhara", which means "mind-conditioner" and is defined in suttas SN 41.6 & MN 44. The feelings of rapture & happiness are the "mind-conditioner" because they condition the mind (citta) in certain ways (such as condition the citta to generate lust, delight, self-views, awe, etc, towards the feelings of rapture & happiness).

The third tetrad is about the citta itself. When the feelings of rapture & happiness are calmed away, what is left is the citta, which includes some possibly underlying defilements that have previously arisen in relation to or conditioned by the rapture & happiness.

Refer to Mindfulness With Breathing: Unveiling the secrets of life: A Manual for Serious Beginners by Buddhadāsa Bhikkhu

You'll want to look at Goddard's translations of mind essence. It's a essential read. A verbal chanted mantra that describes breath counting is essentially what I believe is intended from this text. It's not a short term task nor is it absolution. But it's not something you need read a text and grasp. He's telling you to breathe. Not think but breathe. Breath counting it's essential to a strong beginners form of meditation. You should be alert but an alert mind wanders. Like when your in bed and you think of a chore. You should be asleep. In this case it's the opposite. You should pay attention to your breath but not sacrifice mental efforts. After you master it one way. You flip it. The way I express it matches under the 3 pillars of Zen. Half breathe to ten and recount. After you do this 20 minutes a day without fail which takes weeks to months. You count both in and out. Then you go to the next step. The whole point is the brain would rather do anything other than upload into the ground below your feet and sit calmly. My roshi would have me sit on something uncomfortable so I would pay attention. If you're washing with your breath you're healing from your abuse as long as you put it down while meditating. You actually have a bigger problem then you understanding of this I'd recommend you focus on. If I point to the moon and say: "Look! The moon!" as I'm standing in front of you. Don't look at my fingers that's not the point. You really need the moon. Not me pointing at it. Self help books will point at others pointing points but it's not unlike the language gaps from transition or the point of generational meaning. Or generally speaking....your trying to learn how to breathe even though as a baby you knew how to breathe. That's not the point. Pay attention to it and don't think too much

He trains himself to breathe in sensitive to mental processes, and to breathe out sensitive to mental processes.

(Cittasaṅkhārapaṭisaṃvedī assasissāmīti sikkhati. Cittasaṅkhārapaṭisaṃvedī passasissāmīti sikkhati.)

He trains himself to breathe in sensitive to the mind, and to breathe out sensitive to the mind.

(Cittapaṭisaṃvedi assasissāmīti sikkhati. Cittapaṭisaṃvedī passasissāmīti sikkhati.)

In MN 44 we find an explanation for cittasaṅkhāra:

"Now, lady, what are fabrications?"

"Perceptions & feelings are mental fabrications." (Thanissaro trans.)

(Saññā ca vedanā ca cittasaṅkhāroti.)

The Visuddhimagga says (VIII, 229ff):

The remaining [three] clauses should be understood in the same way as to meaning; but there is this difference here.

The experiencing of bliss must be understood to be through three jhanas, and that of the mental formation through four. The mental formation consists of the two aggregates of feeling and perception. And in the case of the clause, experiencing bliss, it is said in the Paþisambhidá in order to show the plane of insight here [as well]: “‘Bliss’: there are two kinds of bliss, bodily bliss and mental bliss” (Paþis I 188). Tranquilizing the mental formation: tranquilizing the gross mental formation; stopping it, is the meaning. And this should be understood in detail in the same way as given under the bodily formation (see §§176–85). Here, moreover, in the “happiness” clause feeling [which is actually being contemplated in this tetrad] is stated under the heading of “happiness” [which is a formation] but in the “bliss” clause feeling is stated in its own form. In the two “mental-formation” clauses the feeling is that [necessarily] associated with perception because of the words, “Perception and feeling belong to the mind, these things being bound up with the mind are mental formations” (Paþis I 188). So this tetrad should be understood to deal with contemplation of feeling.

(ix) In the third tetrad the experiencing of the [manner of] consciousness must be understood to be through four jhanas

Ven. Buddhadasa [1] explains that second tetrad as concerned specifically with pīti and sukha whereas the third is concerned with citta in a broader and deeper way.

[1] - Mindfulness With Breathing: A Manual for Serious Beginners