毎(ごと)にEach, Every

Both expressions show frequency, but in different ways. The に (frequency) construction combines a time period with a number to mean '(A) times per (B),' e.g. 一週間に２回 'twice a week'. ごとに attaches to a number + counter to mean 'every X,' e.g. 二時間ごとに薬を飲む 'take medicine every two hours'.

ごとに and たびに both express frequency, and can be interchangeable in cases like 失敗するたびに／ごとに 'every time (you) fail'. However, ごとに can directly follow time or distance expressions (e.g. ３時間ごとに), while たびに requires a verb indicating an action or event, e.g. ３時間が経つたびに 'every time 3 hours pass'. Their noun forms also differ, e.g. 発表の度に vs. 発表ごとに (both meaning 'with every announcement').

ごとに and おきに both express regular intervals, but with a key difference. ２日ごとに means 'every two days', i.e. the event happens on the second day. ２日おきに means 'at intervals of two days', or in other words every third day. A helpful tip: おきに comes from 置く, which can have the meaning of leaving a gap or space.

ごとに and たびに both express frequency, but differ in usage. In phrases like 失敗するごとに or 失敗するにつけ 'every time (you fail)', the meaning is similar, though the grammatical attachment is different. につけ is also more formal and literary, while ごとに is common attaches directly to time or distance expressions, e.g. ３時間ごとに 'every 3 hours'.

Both express regular repetition, but in different structures. ～ずつ attaches to quantity phrases to mean 'each' or 'little by little', e.g. 一つずつください 'Give me one of each.' ごとに follows nouns and means 'every (A)', often time-based, e.g. ３０分ごとに体を動かす 'I move my body every thirty minutes.'

Both phrases express frequency but differ in usage. ごとに attaches to time expressions, nouns, or verbs to mean 'every (A),' e.g. ３時間ごとに 'every three hours' or 失敗するごとに 'every time (you) fail'. まい～のように is used only with time words that take 毎 and adds emphasis, meaning 'almost every (A)', e.g. 毎日のように 'nearly every day'.