Well.. the first kind is repentance at salvation. This is entrusting your salvation with Jesus:
Mar 1:15 And saying, The time is fulfilled, and the kingdom of God is at hand: repent ye, and believe the gospel.
so.. Strong's concordance on repent-
G3340
μετανοέω
metanoeō
met-an-o-eh'-o
From G3326 and G3539; to think differently or afterwards, that is, reconsider (morally to feel compunction): - repent.
So I believe this happens at salvation. Entrusting your salvation with Jesus = repentance.
So this is then done and dusted. Salvation settled and permanent.
Now there is daily repentance.. which is relying on Jesus in your daily walk. This is not a HAVE to.. but comes out of responding to what Jesus has done for you.
repent for eternal salvation is the same as:
(John 3:5) Jesus answered, Verily, verily, I say unto thee, Except a man be born of water and of the Spirit, he cannot enter into the kingdom of God.
It is a change of mind.. with the mind being:
G3563
νοῦς
nous
nooce
Probably from the base of G1097; the intellect, that is, mind (divine or human; in thought, feeling, or will); by implication meaning: - mind, understanding. Compare G5590.
G5590
ψυχή
psuchē
psoo-khay'
From G5594; breath, that is, (by implication) spirit, abstractly or concretely (the animal sentient principle only; thus distinguished on the one hand from G4151, which is the rational and immortal soul; and on the other from G2222, which is mere vitality, even of plants: these terms thus exactly correspond respectively to the Hebrew [H5315], [H7307] and [H2416]: - heart (+ -ily), life, mind, soul, + us, + you.
G1097
γινώσκω
ginōskō
ghin-oce'-ko
A prolonged form of a primary verb; to “know” (absolutely), in a great variety of applications and with many implications (as shown at left, with others not thus clearly expressed): - allow, be aware (of), feel, (have) known (-ledge), perceive, be resolved, can speak, be sure, understand.
So.. repentance equals a change in mind.. which equals a change in perception, understanding, knowledge.. and is related to the spirit of person..
compare this then with:
(Eph 1:13) In whom ye also trusted, after that ye heard the word of truth, the gospel of your salvation: in whom also after that ye believed, ye were sealed with that holy Spirit of promise,
Greek word for believe:
G4100
πιστεύω
pisteuō
pist-yoo'-o
From G4102; to have faith (in, upon, or with respect to, a person or thing), that is, credit; by implication to entrust (especially one’s spiritual well being to Christ): - believe (-r), commit (to trust), put in trust with.
This looks alot like repentance to me