In the book "Einstein Never Used Flashcards" they recommend two counting development observations. One for one correspondence where you observe your counting toddler counting each item in a group and only counting it once. Then there's number order where even if the numbers are "wrong" they always count in the same order.
Basically, going 1, 2, 4, 7, 3 for a group of 5 objects and 1, 2, 4 for a group of 3 objects is a more real form of counting than counting 1, 2, 3, 4, 5 for all sizes of groups. Always saying 12345 or 12345678910 when asked to count means that the child has memorized that phrase.
If your toddler counts 1, 2, 3, 4, 5 when there are 5 objects, and 1, 2, 3 when there are 3 objects, he is in fact, counting.
Eta: it sounds like he's in a developing stage. You should watch for him to start using one for one correspondence and number order, it'll be cool for you to see that develop (typically between ages 2 and 4). Then later on (4 to 6 or so) you'll see him start to "count on" where if he's already counted a group and you give him another one he'll just keep counting the new things instead of recounting the whole group. (What you'll see first is "1, 2, 3, 4....1, 2, 3, 4, 5, 6" then "1, 2, 3, ....4, 5, 6")