Unless mentioned specifically you should assume that AES calculators will perform all the calculations necessary to implement the block cipher.
Beware that sometimes these calculators also use a mode of operation and a padding mode, often without mentioning it. They may also provide encodings without mentioning it.
Personally I distrust most online calculators for these reasons. I would rather use Java to be able to configure everything as required, or use tools such as OpenSSL command line (with the explicit -K and -iv parameters).
The one you show performs all the 10 required rounds for AES. It doesn't use any mode of operation (such as ECB or CBC) or related padding mechanism. It is rather sensible as it uses hexadecimal encoding for all values (key, input and output) and mentions it explicitly as well.
For a single round result you can use the crypttool which kelaka pointed out in the comments section. Please make sure that you select one round and disable "chaining". It would be tricky to explain the other options without explaining AES itself; I would suggest to read into AES and only use the options after they have been explained to you.