The single most useful thing to know about Shinto purification is that what is being removed is not guilt.
Kegare is defilement: a condition contracted through contact with death, blood, illness or decay, regardless of intention and regardless of fault. A person who has attended a funeral is polluted. A person who is bereaved is polluted, which is why in traditional practice a bereaved family did not visit a shrine during mourning, and part of why Shinto has historically left funerals to Buddhism. None of this implies wrongdoing, and treating it as a moral category produces immediate and serious misreadings.
Tsumi is nearer to transgression, and the old catalogues of it are revealing. They include breaking irrigation channels and skinning an animal backwards alongside offences a modern reader would recognise as such, and they also include leprosy and being struck by lightning. Misfortune and misconduct appear in the same list, which is what a category of pollution looks like before anyone has moralised it.
Because the condition is a state rather than an act, it is removed by procedure rather than by repentance. Rinsing, waving a wand, transferring the impurity to a paper figure and destroying it: these work in the way that washing works. There is nothing to confess and nobody whose forgiveness is required.
This is one of the clearest cases in comparative religion where an obvious-looking parallel is false. Christian confession and Shinto purification both restore a person to a fit state before approaching the sacred, and they are addressed to entirely different problems.