LFJ is right, technically speaking
The real rub is the term 'monk'. What LFJ is defining is a bhikṣu, which is a very specific title for a Buddhist monk. Now here's the rub. While a Shaolin monk is, technically speaking, a Buddhist monk, there's this huge grey zone with the wuseng and biaoyanseng. Technically speaking, as LFJ points out, these classes of adherents are actually just secular disciples, not fully ordained bhikṣu. However, the definition of 'monk' is merely a male member of a monastic order. It is not bound by the tenets of Buddhism. It is a multicultural term. Out in the world at large, the wuseng and biaoyanseng are called Shaolin monks, even though they are not bhikṣu. So where does that leave the Shaolin order? And more specific to this discussion, where does that leave the non-Chinese Shaolin disicples? Heck, I'm a sujiadizi and I've performed kung fu at Shaolin for tourists. Can I start calling myself a Shaolin monk?*
This situation only really exists at Shaolin. Shaolin is very unique obviously.
*Actually I call myself the 'real fake monk' sometimes, mostly in honor of this situation. ;)