This happens very often in many companies. I think I'm at a very early stage of my career and I'm still unsure how should react to this scenarios.

Say you are a developer on a team of 4 members, your manager is busy most of the time dealing with other stuff as he has more teams or other activities, hence he struggles to give the dev team enough of his time. He talks with a member and offers him to move him to a "lead developer role". This implies the member will start managing the team in all administrative aspects, coordinate the development BUT still be coding. Although this represents career development at the moment your salary will remain the same. Of course (like everywhere) you are promised that if you do good you might get an official position and get a raise.

What should one do in these situations?

Accept more responsibilities knowing you are basically doing this for free but it will help you to gain experience
or
Deny the offer. You are already doing hard work. That's why the picked you. It looks like they are trying to get the most of you and giving the least they can.

NOTE: There is no possibility of a written agreement that will guarantee that you would get official position in the future.