I think long story short: the difference between (lim) and not is that the dominant step drives the limiting case more strongly than the non-limiting case.
There are two aspects to a substitution reaction:
- Stoichiometric mechanism: the sequence of elementary steps that take us from reactants to product
- Associative (A): the bond formation between the metal and the entering ligand i
- Dissociative (D): the bond breaking between the metal and the exiting ligand is the important step, i.e. the intermediate has a decreased coordination number
- Interchange (I): there is no evidence of an intermediate
- Intimate mechanism: what affects the rate constants of particular steps?
- The reaction rate is affected by the entering group (a)
- The reaction rate is affected by the leaving group (d)
You can see that SN1 and SN1 (lim) both have dissociative intimate mechanism, which means that the breaking of the bond between the metal and the leaving group is the rate determining step. In SN1 (lim), the leaving ligand bond breaks first forming an intermediate with a lower coordination number; the entering ligand then forms a bond with the metal. However, SN1 is an interchange stiochiometric mechanism which means that there isn't a true intermediate where the leaving group has totally left. In this case you could imagine that the leaving metal-ligand bond merely weakens or 'stretches' before the incoming ligand bonds to the metal.
Similar principle applies to SN2 (lim) and SN2. In SN2 (lim), an intermediate with higher coordination number is formed when the entering ligand bonds with the metal. For SN2, no such intermediate step is observed. You could say that the incoming ligand simply begins to form a bond to the metal before the leaving group bond starts breaking.
(http://nptel.ac.in/courses/104106063/Module%205/Lectures%208-10/Lectures%208-10.pdf for image above)