okay I explain you in my way !!
Complete lattice means partially ordered set in which all subsets have both a join and an meet
Bounded Lattice means In a lattice if upper bound and lower bound exists then it's called bounded lattice
every complete lattice is Bounded lattice is easy to analyze by the definition of Complete lattice
But every bounded lattice is not complete lattice is the real deal here
M = {a $\varepsilon$ Q } where - $\sqrt{3}$ < a < + $\sqrt{3}$ Q---- > rational number
it's bounded right ???
Now in this Hasse Diagram can you tell me that what it's element at the Top position (dot at the top ) which is less than $\sqrt{3}$ and what it's GLB ??
you can't tell that right ??? because there's a infinite numbers
Though you may have a set which have Greatest and lower bound but its doesn't mean that the subset will have these lower and upper bound
remember : whenever there's a infinite sets ---- > it's not a complete lattice