Big-O is an upper bound.
Big-Theta is a tight bound, i.e. upper and lower bound.
When people only worry about what’s the worst that can happen, big-O is sufficient; i.e. it says that “it can’t get much worse than this”. The tighter the bound the better, of course, but a tight bound isn’t always easy to compute.
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The following quote from Wikipedia also sheds some light:
Informally, especially in computer science, the Big O notation often is permitted to be somewhat abused to describe an asymptotic tight bound where using Big Theta notation might be more factually appropriate in a given context.
For example, when considering a function T(n) = 73n3+ 22n2+ 58, all of the following are generally acceptable, but tightness of bound (i.e., bullets 2 and 3 below) are usually strongly preferred over laxness of bound (i.e., bullet 1 below).
T(n) = O(n100), which is identical toT(n) ∈ O(n100)T(n) = O(n3), which is identical toT(n) ∈ O(n3)T(n) = Θ(n3), which is identical toT(n) ∈ Θ(n3)
The equivalent English statements are respectively:
T(n)grows asymptotically no faster thann100T(n)grows asymptotically no faster thann3T(n)grows asymptotically as fast asn3.
So while all three statements are true, progressively more information is contained in each. In some fields, however, the Big O notation (bullets number 2 in the lists above) would be used more commonly than the Big Theta notation (bullets number 3 in the lists above) because functions that grow more slowly are more desirable.