You are right, it’s the same thing 
So stat wise (these are approx ones):
Comanche Raider (rifle rider)
Age III unit
18-20xp
200hp
20% melee resist
7.25 speed
15 LOS
16 attack x3 vs heavy cav and inf, x2 vs artillery 1.5 RoF
12 Range
13 siege attack 3 RoF
A decent visualisation from Empire: Total War
Comanche lancer:
16-18xp
250hp
20% ranged resist
6.75 speed
15 LOS
25 attack x1.5 vs heavy inf 1.5 RoF
25 siege 3 RoF
I’d say visually a leather wearing rider with bonepipe on painted horse with lance and possibly a shield as a coup rider has. Kinda like:
Buffed Horse Archer:
18xp
200hp
10% melee resist
7.25 speed
16-18 LOS
20 attack x1.5 vs settlers x2 vs heavy cav 1.5 RoF
15 siege attack
As I said, stats are only approximated to show the purpose of given unit, not perfectly balance them (Raider similar to Rifle riders, Lancer a bit like faster, weaker spanish lancer and a decent horse archer, good against villies).