Japanese Stones and some context
This is a huge subject so below are some descriptions from our friends at the Japanese Garden Directory

boat stone
A garden stone shaped like a ship. It is placed in a pond, or on the white sand representing a water surface in a dry landscape garden. The one at the garden at the shoin of Daisen'in temple is well known.
stone arrangement
The aesthetic arranging of stones to compose the main structure of the garden or a landscape forming one of its major parts, an important skill in making Japanese gardens. This term is also used to denote arrangements of stones made in this manner. It is also called iwagumi.
preeminent ornamental stone
An ornamental stone of outstanding value, which is appreciated entirely on its own.
ornamental stone
A garden stone which can be appreciated for its own value. There are cases when several such stones of the same material are arranged together.
discarded stone
1. A stone seemingly placed in an offhand manner in a garden. It is one of the important key stones placed at a strategic position, despite its low value as an ornamental stone.
2. In a tea garden, a stone placed beside a stepping stone and a little bit apart.
purifying stone
A key stone with a low and upright shape, placed at the screen fence side of a veranda water basin. It is also called kiyome ishi.
round stone
A stone generally taken from the bed of a river, round in shape and about 15-30 cm in diameter. The type of material is not relevant. In gardens they are used in nobedan pavements, for stone-paved beaches, as well as stone walls.
sitting stone
One of the key stones mentioned in Tsukiyamateizōden (zenpen). According to that work, it is placed on the Master's Isle. It is supposed to be used in a way similar to the stone of easy rest.
snail stone
A large stepping stone used as a path junction stone. The name is said to be based on the resemblance to a gigantic snail in shape, but is thought in fact to derive from the term for an old temple stone, which has the same pronunciation.
statue stone
One of the five basic stone shapes described in Ishigumisonō yaegakiden. A tall standing stone, it is used in the center of the garden landscape.
stone of amusement
One of the key stones mentioned in Tsukiyamateizōden (zenpen). According to that work, it is placed on the Master's Isle. It is supposed to be good for anglers to sit upon
stone(s) of the nine mountains and eight oceans
The whole world is composed of nine mountains and eight oceans, according to the Buddhism cosmic view expressed in the myth of Mt. Sumeru. In representing this Buddhist image in the garden, a stone arrangement may be made symbolizing the nine mountains and eight oceans, or a single stone called kusen hakkai ishi is placed in a pond. The stone of the nine mountains and eight oceans in the Kyōkochi pond at Rokuonji temple (Kinkakuji) is well known.
stones of the sixteen journeying priests
A stone arrangement or distribution of stones which symbolically represents sixteen journeying priests. It is seen principally in gardens of Edo period temples.
stones of the two gods
Key stones mentioned in Tsukiyamateizōden (zenpen). According to that work, they are a pair of standing stones placed on level ground near the entrance of a garden. They are also called niōseki.
summit stone
One of the key stones mentioned in Tsukiyamateizōden (zenpen). It is placed near the summit of an artificial hill.
sword-hanging stone
A key stone upon which one stands to hang one's sword on the sword rest attached to the outer wall of the tearoom. A double-stepped stone with a good shape is often used, to ornament the area beneath the eaves.
tail stone
One of the key stones comprising the stone arrangement of tortoise island. It represents the tail of the tortoise.
tortoise island
A representative form of island in pond gardens or dry landscape gardens. Under the influence of the Chinese cult of immortality, it came to be made together with the crane island in hope for long life and happiness, and was frequently built from the Muromachi to the Edo periods. It is composed of a tortoise head stone, foreleg stones, hind leg stones, and a tail stone.
Some books on the subject available from Amazon
Japanese Stone Gardens: Origins, Meaning, Form
Hardcover – 10 Sept. 2017by Stephen Mansfield (Author), Donald Richie (Author)
The Art of Setting Stones: & Other Writings from the Japanese Garden
Paperback – Illustrated, 17 Oct. 2002by Marc Peter Keane (Author)