The terms 'baby' and 'toddler' would not be used of a child simultaneously but because of their vagueness might overlap if applied logically. Some sources give definitions by age that do not overlap, but that is an artificial division.
- a baby (or synonymously an infant) is a child that has just been born and cannot yet talk (incidentally to around 1 year old when they start to talk)
- a toddler is a child that has just learned to walk (and this incidentally occurs around 1 year of age)
The upper limit between a toddler and just a very young child is much vaguer, I think of it as literally when the child is well-balanced (that is not 'toddling' any more). A four year old doesn't seem to be a toddler any more but a three year old might be. Even a two year could get away with not being a toddler and instead just a very young child.
But despite the logical fact that one might be able to talk but not yet able to walk or walk and not talk (in the varying ways that abilities develop in a child), one would be hard pressed to label a child both a baby and a toddler. If you can walk, you're not a baby any more, you're a toddler. If you can speak but can't yet walk, you'd probably still be labeled a baby (though maybe not an infant).