I've seen the term 'unlimited' and 'infinity' used interchangeably in non-standard analysis. However when reading a scientific american magazine (Nov 1994 - "Resolving Zeno's Paradoxes") the author says this:

I am slightly confused. Which is it? I can't see why the inverse of an infinitesimal would be infinite if 'unlimited' and 'infinite' actually had the same meaning.Because an infinitesimal is very small, its inverse will be very large (in the standard realm, the inverse of one millionth is one million). This type of nonstandard number is called an unlimited number. The unlimited numbers, though large, are finite and hence smaller than the truly infinite numbers created in mathematics. These unlimited numbers live in a kind of twilight zone between the familiar standard numbers, which are finite, and the in-finite ones.