This is the current Japanese Card Rarity list that is updated with Sword & Shield TCG.
Also includes the Japanese wording of each rarity and how to pronounce these in Japanese.
Please mind there is no official information about card ratios other than the guaranteed 1 SR or better per box. These card ratios are only estimations and is subject to change.
RR - Double Rare
ダブルレア - Dabururea
This is the most common rarity for V cards. You can recognize them by the glossy embossing effect.
You can get up to 4-5 RR V cards per box.

RRR - Triple Rare
トリプルレア - Toripururea
This rarity has been introduced during S1H / S1W Sword & Shield and so far is only exclusive for VMAX V Cards. These are textured cards similar to SR cards.
You can get up to 1-3 RRR VMAX Cards per box.
Update 9-7-2020: With S3a Legendary Heartbeat, when you pull a VMAX Card, you also get the matching V card in the same pack. This was meant so you could build a (Pre-release style) deck in the Charizard VMAX HR competition, instead of having a VMAX card you couldn't use.

SR - Super Rare
スーパーレア- Sūpārea
This rarity is often mistaked with Secret Rare, technically they are secret rare cards in Japanese sets, since they exceed their set number, but it's officially called Super Rare.
These are usually Pokémon V cards or Supporter cards and are textured.
You get 1 SR card or better per box guaranteed, and maybe 2 SR cards or better per box.

SSR - Unknown Name
Could be Shiny Super Rare, the official name is not confirmed yet.
Shiny Pokemon are appearing as SR cards. Not all Pokemon are available, nor are all Pokemon included in this pack. Only some selected Pokemon are included as SSR. There are various rumors about whether it is a double Super Rare or a Shiny Super Rare, but it is still unknown.
In SM8b GX Ultra Shiny you were guaranteed 1 GX SSR card per booster box, this is the same for S4a Shiny Star V.

S - Unknown Name
Could be Shiny or Secret, the official name is not confirmed yet.
Similar to SSR cards, Shiny Pokemon are also appearing in S4a Shiny Star V. Not all Pokemon are available, nor are all Pokemon included in this pack.
Only some selected Pokemon are included as S cards. Since S cards lack the SR wording, we are curious what it will be called.
In SM8b GX Ultra Shiny you were unofficially getting around 2-3 S cards per booster box, this is the same for S4a Shiny Star V.

HR - Hyper Rare
ハイパーレア - Haipārea
Hyper Rare cards, SR or RRR cards with a rainbow colour and different texturing.
Starting from Sword & Shield, these cards contain a glitter effect and Supporter SR cards also have been added.
In the same slot as the guaranteed SR card in 1 box.

UR - Ultra Rare
ウルトラレア- Urutorarea
These are Gold Cards. Starting from Sword & Shield, these also contain a glitter effect.
Usually these could contain Item, Tool, Stadium, Energy or Gold Pokémon V cards.
Starting from S1a VMAX Rising, Shiny Non-V Cards from sets also have been added to this rarity.
In the same slot as the guaranteed SR card in 1 box.
In S4a Shiny Star V, Black & Gold UR cards of Zacian V, Zamazenta V, Eternatus V and Eternatus VMAX were introduced. These are in the same alot as S cards outside of the guaranteed SSR V/VMAX cards.

A - Amazing Rare
アメイジングレア - Ameijingurea
Introduced in S3a Legendary Heartbeat, these are also textured.
You can get up to 1 Amazing Rare Card per box (unofficially confirmed).

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Comments
THANK YOU. This is super helpful.
I got a card with a K rarity. Can you explain what that one is?
Nice! You have a radiant card from battle region
It's said that the K rarity is apparantly derived from the japanese word >Kagayaku< which translates to radiant along with 10 other variants of the word for example glitter, shine, sparkle, glow
Are UR cards more rare than SR at the end of the day or there's isn't a noticeable difference?
What is the rarity of a Japanese card that doesn’t have anything next to the card number? E.g. A non-holo Eevee card simply has s8b [E] 125/184. Thanks!