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A car seat or a park seat has two main parts. One part is the back, against which one leans their back. What is the name of the part that one actually sits on (puts their buttocks on it)? For a chair these two are called back and seat respectively. But what about a car seat or a park seat?

One word for a the part of a car seat that you sit on is squab.

1

a : couch

b : a cushion for a chair or couch

Merriam-Webster

That centre front seat slides all the way back until it hits the rear-seat squab, so a child can still sit ‘in the front’, but remains sufficiently rearward not to be hit by an airbag designed to restrain an adult.

ODO

The word isn't applicable to a park bench because generally they aren't cushioned. I've only seen it used in reference to car seats, although dictionaries imply that it can be used of any seat cushion. It's not normally used for the back cushion (even though ODO does mention that).

I found a diagram illustrating a car seat and its components for a Programmable seat back damper patent

The cushion where the driver or passenger sits on is either called a horizontal cushion or seat cushion. The back of the car seat (No.16) is called the seat back but it can also be referred to as a backrest.
A support for a person’s back when they are seated _{Oxford Dictionaries}

The seat 12 includes a generally horizontal seat cushion portion
or seat cushion 14 and a generally upright seat back portion or
seat back 16 pivotally connected to the seat cushion 14 by a seat back pivot 17. The seat cushion 14 includes a seat pan (not
shown) and a cushion 18 operatively connected to the seat pan by
suitable means such as an adhesive. The seat back 16 includes a seat
back frame (not shown) and a cushion 20 disposed about and operatively
connected to the seat back frame by suitable means such as an
adhesive. (...)

Perhaps the OP was thinking of a bench seat of a car when he mentioned a park seat. It is a term which I was unfamiliar with, so I decided to include it anyway.

Bench seat

The bench seat was the traditional seat installed in American and
Australian automobiles. This seat featured a continuous pad running
the full width of the cabin. The second row of seating in most sedans
is usually a bench. The third row of most SUVs and minivans, which may
be forward, or rear facing is also a bench seat.

^{Source: Wikipedia}

In general upholstery usage, the squab is a thickly padded cushion one sits upon, contacting the thighs and buttocks, especially a cushion for two or more to sit upon. This includes the lower portion of a bench if that lower portion is thickly padded. In North America, the same usage is maintained in the automotive industry. In England, the same applies in home and hospitality usage, but is reversed for automotive usage. In England during the middle and late twentieth century , squab in automotive usage, refers to the backrest portion of the chair or backrest portion of a bench, or side supports one may lean upon. As England moves into the 21st century, some still call the automobile backrest cushion a squab while most now call the seat bottom cushion a squab. This leads to a lot of confusion and some incorrectly ordered car parts in England. Notice Oxford Dictionary Online defines an automobile squab explicitly as the backrest portion cushion; it then cites three usage examples which, all three, unmistakably refer to the SEAT BOTTOM portion! An absolute contradiction! I am reminded of an English piece of literature "Alice Through the looking Glass". I was taught upholstery by an English craftsman who was very stiff about correct word usage.