no, you aren't the same.

I've noticed, recently, something I do and something others do. A lot. 

In an effort to be empathetic (it would appear) we try to equate something we've been through with something someone else has been through. 

An example (pretty obvious) would be along these lines: 

Person: We have no money to pay our bills. 
Me: Yeah, I once had to sell my jeep to pay off some debt. 

Person: I've been sick for three weeks. 
Me: Oh man, my dad has the same thing. 

These, of course, can be fine responses. But, there is a dark side. 

Don't expect me to help. I've been through the same thing and I got through it. So, you'll be fine just like I am now, and I got here without your help, by the way, so don't expect mine.

Of course, it's never said that way but it's easy to interpret that way. The attempt at empathy is actually very non-empathetic, even cold. 

The answer, as usual, is to simply listen more. Tell me more. What's that like. What can I do? 

And then instead of excusing ourselves because we've been through something similar, after hearing some good options from them, help where we can.