Like much of the written language found in Japanese history, the counting and number system that is used was imported from China upwards of one thousand years ago. The modern Japanese number system is essentially the same as Chinese except for pronunciation. There is a native counting Japanese system, however it is very rarely, if ever, used.
Next is the difference between numbers and counting. The use of numbers for counting from 1 to 10 treats the numerals as mathematical entities, simply representing an abstract concept. Counting is for actual, tangible objects, like counting the quantity of objects that are being bought. Just for reference, both are included below.

1: ‘Ichi’ (pronounced ‘each-ee’); as a counter ‘hitotsu’
2: ‘Ni’ (pronounced ‘knee’); as a counter ‘futatsu’
3: ‘San’ (pronounced ‘sun’); as a counter ‘mittsu’ (pronounce both t’s, thus holding the ‘t’sound for a moment before continuing to ‘su’.)
4: ‘Shi’ (pronounced ‘she’); as a counter ‘yottsu’
5: ‘Go’ (pronounced ‘go’ but very short); as a counter ‘itsutsu’
6: ‘Roku’ (pronouncing it as ‘loku’ is actually closer to native pronunciation); as a counter ‘muttsu’ (pronounced “moot-tsoo”)
7: ‘Shichi’ (pronounced ‘shee-chee’); as a counter ‘nanatsu’
8: ‘Hachi’ (pronounced ‘hutch-ee’); as a counter ‘yattsu’
9: ‘Kyu’ (just like the letter Q); as a counter ‘kokonotsu’
10: ‘Ju’ (pronounced ‘jew’); as a counter ‘toh’