Count to three.
On the count of three.
Are they the same thing?

See a translation

Both statements have the same literal meaning. However, their grammatical functions are slightly different.

Count to three --> Just as it is now, this is order. This is because, in English, when omitting the subject of the sentence, the sentence becomes imperative. However, if you add a subject, such as 'I count to three' or 'Let's count to three,' it's no longer an order but a statement.

On the count of three --> This is a phrase and is not an order. You can use this in a sentence such as "Let's run on the count of three." In this sense, 'count to three' cannot modify a sentence but 'on the count of three' can modify a sentence.

Hope this helps!