As you said, it's a speed controller. You have power in and power out, nothing (much) more.

If you want an alternative to a sabertooth there are a few out there, robo claw for example. But, 1) I think the robo claw is discontinued now and 2) The robo claw on Amazon is $199 which may be more expensive anyway.

Unfortunately there isn't a cheap, reliable 60A controller. You can pick 2 of the three key points, cheap/60A wont be reliable, cheap/reliable wont be 60A and reliable/60A wont be cheap.

what exactly is a job of a sabertooth

Sabertooth is a brushed DC motor controller... you'll need a motor controller for your mobile robot unless you are using continuous rotation servos... in which case you can drive them straight from most micro controllers including the EZB (meaning no motor controller needed for continuous rotating servos)...

Do you really need to pull up to 60 amps?

I don't know. It is for my Jazzy wheelchair. I saw one made for dual 12A, dual 25A. Then of course the 60A.

can this controll motor too. motorcontroller

Find out the max current draw of the motors before you look for a motor controller/driver. Then pick a motor controller/driver to suit the load.

If you don't want to blow things up or spend more than you need to it is a very important step to take. I always either look up or measure the current draw on any item I am using, it's just good practice and common sense to be honest.

@nomad18.08 that is a basic 2A L298n based H-Bridge, it's what many use for Omnibot and smaller motors. Wheelchair motors are more than likely going to be more than 2A so that wouldn't work in this case.