What is the equivalent method of practicing tactics methodically in
chess?
Would it be to practice one motif repeatedly? Or is it to
practice blitz+standard?
Preface
Playing standard games goes along with tactics training, but clearly not a part of tactics training at all. Many masters use blitz games as part of tactics training; but whether you should use this practice depends on your experience.
(Quote from https://thechessworld.com/articles/training-techniques/10-little-known-chess-training-methods-that-work/)
A moderated amount of blitz, online or over the board, can help you
keep sharp. Be aware, an overdose of blitz can literally destroy your
chess thinking and turn you into a superficial player with very little
chances of survival in longer time controls.
If you tend to play too fast in standard games (much less aware than usual) after playing blitz games, I recommend not playing blitz games at all (see the above quote as to why).
Tactics Training
Tactics training is not just one practice; it is rather comprised of a number closely related practices, each aiming one/more of the following:
(1) Get familiar with a theme (or a motif for that matter)
(2) Spot important themes in a given position
(3) (Tactical) alertness training
NB: I recommend doing them in the given order, that is Practice (1), followed by Practice (2) and finally Practice (3).
Practice (1)
Practice (1) is done especially when someone learns a theme for the first time. In (1), the player practices a large number of (relatively easy) puzzles of the same theme in one stretch. This can be done with tactics books where there are exercised arranged by theme, or with websites (such as lichess.org) that allow tactics training by theme.
The aim of practice (1) is recognition of a pattern (in simplest setting, at first). Here, the focus is on recognizing the pattern in a large number of puzzles in reasonable time (rather than doing a few hard ones). The hardness level of the set of puzzles can be gradually increased, as long as the player is still able to solve a large number of puzzles in reasonable time (the principle at play here is reward).
Practice (1) can be repeated spaced out a la spaced repetition method with or without targeting to reduce the time taken to solve the problem (the latter is the focus in the woodpecker method explained in Brian Tower's answer). Both spaced repetition and the woodpecker method seem to recommend using the same set of puzzles multiple times in order to learn the set of puzzles basically by heart. I personally recommend against it. I think using a very similar set of puzzles would be more beneficial (how similar works best is a topic worth researching). This is my recommendation because the aim is to get familiar with a particular pattern, not a particular position. At the least, one can make small changes in less relevant parts of the position (relevant relative to the pattern at hand). The downside of this is that you need someone to prepare similar sets of puzzles unless
(i) you are using a website that allow practicing puzzles by theme as well as rating level, or
(ii) you have a large set of puzzles along with hardness level and splitting it up into almost equal smaller sets is easy.
Practice (2)
Practice (2) is the most commonly available one. Some basically identify tactics training with practice (2). In (2), you are given a position where there are some tactical possibilities (opportunities or threats), and you have to find the best move. Quite often, (2) is a testing ground for familiarity with tactics and also the ability in calculation. Besides, practice (2) tests a player's ability to weight different factors based on their relative importance in the given position.
Practice (2) is doable with a large number of chess books (exercises not by theme) and websites such as chess.com, lichess.org, chesstempo.com, etc.
In (2), more often than people realize, mixed tactics/themes is at play. For example, even in tactics training by theme (i.e., (1)), if two puzzles differ in hardness level, say puzzle 2 is harder than puzzle 1, then almost always puzzle 2 involves a larger number of other themes and/or themes at a higher level (different themes involved are usually missed since some themes are less appreciated than others; e.g.: gaining tempo, coercion, reloader, attack/remove the defender, opening/closing lines, trapping pieces).
Practice (3)
Many players find it easy to solve puzzles, but unable to spot easier ones in their games (see this question for instance). Practice (3) addresses this issue. Here, a set of positions are given, and the question is "What is your move in this position?". A position in the set may or may not involve a tactic, and it may have more than one answers (e.g. depending the plan the player comes up with). This simulates the game situation more closely.
A set of positions with this idea can be found here.
Also, a set will be timed and the player is asked to solve the maximum number of puzzles within the specified time (time should not be too low). Here, not only calculation, but also judgement is tested. The player has to decide which positions require a more thorough calculation. There is no guarantee that there is tactical resource for you (e.g. no automatic sacrifices). Deciding when to calculate deeply is a crucial skill for a serious chess player.
Although there are websites that attempt to do practice (3), their success in doing so is questionable (they succeed better when the number of themes involved in the set is larger and also involve positional themes in addition to tactical themes).
It seems to me that puzzles in chesstempo.com have this nature more compared to those in chess.com and lichess (note that choosing tactical positions from games does not simulate game situation).
I think a coach can do the job of preparing a set of positions for practice (3) much better (for this practice, only themes the player is closely familiar with should come up in the given position).