ままに (As Is)As is, While remaining, Left in a state

Both patterns use まま, but れる・られる + ままに expresses acting in line with orders or circumstances, e.g. 言われるがままにする ('Do exactly as told'). In contrast, standalone まま(に) is used in a wider range of contexts to express an unchanged state, e.g. 窓が開けたままになっている ('The window is still open'). The compound implies passivity; the base form, a persistent state.

てある and まま(に) both describe continuing states, but differ in nuance. てある implies an action was done for a reason and that the result remains. For example, 窓が開けてある ('The window has been opened.') implies that it has been left open for a purpose. In contrast, まま(に) emphasizes that the state remains unchanged, without implying purpose, e.g. 窓を開けたまま家を出てしまった ('I left the house with the window open.').

まま(に) and っぱなし both describe something left in a certain state, but differ in tone. まま(に) can be neutral or passive, e.g. 電気をつけたまま寝た ('I fell asleep with the light on'). っぱなし adds a careless or irresponsible nuance, as in ドアを開けっぱなしにしないで ('Don't leave the door wide open').

きり often marks an action done once and left that way, as in 去年会ったきり連絡がない ('I haven't heard from them since we met last year'). まま(に) marks an ongoing unchanged state, as in 靴を履いたまま入らないで ('Don't enter with your shoes on'). Both can imply continuation, but きり emphasizes a cutoff point.

Both expressions refer to a persisting state, but differ in nuance. With たなり・なり, there's often (but not always) an implication that the situation is undesirable or unexpected, as in 部屋に入ったなり出てこない ('Ever since going in his room, he hasn't come out'). まま(に) also marks an unchanged state, e.g. 窓が開けたままになっている ('The window is still open'), but is more neutral in tone.

まま(に) can suggest a condition continuing unchanged or doing something exactly a certain way, e.g. 指示されたままに動く ('Act exactly as instructed'). 如く・如き・如し express resemblance, e.g. 夢の如く消えた ('It vanished like a dream'). Both can involve comparison, but only 如く emphasizes similarity, and is far more formal/literary than まま(に).