The "terrible twos"--is this it?

I think two months ago I was saying, she's started her "terrible twos".  The tantrums and meltdowns for no apparent reason.  Two months later, add her refusing to sit in a shopping cart because she wants to get out and explore or push the shopping cart herself.  This means she doesn't like sitting in anything confining i.e. high chair, car seat, stroller because she wants to get out to explore.  For my birthday, we went out to eat and before entrees came out, we had to pack it to go as she was screaming to go out and explore.  This must be the terrible twos.  I'm sure next month I'll be saying, no, now this is the terrible twos.  This is a normal pattern, no?