Earlier and lately
These point back into the past, from a moment ago to long ago, and all fit the same 'sore ... kiita' frame.
sakki
a moment ago, earlier
さっき
Refers back to something earlier today, anywhere from seconds to a few hours ago.
sore sakki kiita.
I heard that a minute ago.
それさっき聞いた。
sore wa sakki kikimashita.
I heard that a minute ago.
それはさっき聞きました。
Staff and business speech say sakihodo. sakki is fine with desu/masu.
kono aida
the other day
この間 このあいだ
Points to one recent past occasion, days or weeks ago (kono aida itta mise = the place we went the other day).
sore kono aida kiita.
I heard that the other day.
それこの間聞いた。
sore wa kono aida kikimashita.
I heard that the other day.
それはこの間聞きました。
Casually it is often squeezed to konaida (sore konaida kiita). kono mae means the same, and senjitsu is the formal version. kono aida wa arigatou thanks someone again for last time, and Japanese speakers expect it.
saikin
lately, these days
最近 さいきん
Covers the recent stretch up to now, for trends, current life and recent news (saikin isogashii).
sore saikin yoku kiku ne.
I keep hearing that lately.
それ最近よく聞くね。
sore wa saikin yoku kikimasu ne.
I keep hearing that lately.
それは最近よく聞きますね。
saikin dou? is the stock 'how have you been?'.
mae
before; ago; previously
前 まえ
Refers to an earlier time: mae ni (before, once before), mae wa (used to), and a time span + mae for 'ago' (ni-nen mae).
sore mae ni kiita.
I've heard that before.
それ前に聞いた。
sore wa mae ni kikimashita.
I've heard that before.
それは前に聞きました。
The same word means 'in front' (see mae / ushiro). -mae ni after a verb has its own card.
mukashi
long ago; in the old days
昔 むかし
Frames the distant past and old habits (mukashi wa yoku itta = I used to go a lot). mukashi kara means 'for ages'.
sore mukashi yoku kiita.
I used to listen to that a lot.
それ昔よく聞いた。
sore wa mukashi yoku kikimashita.
I used to listen to that a lot.
それは昔よく聞きました。
mukashi mukashi opens folk tales ('once upon a time').