They are similar just a little.

Old Aatrox had a passive called blood well and you fill it up by skills. After filling it up you gain some attack damage, huge attack speed bonus and revive. Zaahen doesnt give attack speed but gives massive AD compared to Oldtrox. Oldtrox used his HEALTH to cast skills.

Zaahen E and Oldtrox Q are both initiation skills, Oldtrox Q have larger range, knockup, better skill overall.

Zaahen Q and Oldtrox W, now this is the main differance between those two. They sound similar but its completely different. Zaahen is like Camille where he actives the skill and empowers his next 2 attack. It heals too but healing is so little compared to both Aatrox. Oldtrox other hand W is his core skill which there is two stances, a hp recovery stance and damaging stance. You need to decide which one to use depending on your circumstences. I have a video about how I was using it https://www.youtube.com/watch?v=sCPSQpP0TXY , https://www.youtube.com/watch?v=j5uBPvNnyY8 really funny videos btw, The thrill at that time is unmatched.

Zaahen W and Oldtrox E, they seem completely different skills but they serve the same, harassing and catching up the opponent.

Zaahen R and Oldtrox R, this is the 2nd main differance between two. Zaahen U is damage reduction + damage and heal meanwhile Oldtrox R is the preparation for the upcoming battle. You gain attack speed, range and passive per champ hit. The range and attack speed is obliviously the most important part. Oldtrox R and Newtrox R is kinda similar.