The general concept of an Sn2 vs. Sn1 reaction is that in an Sn1 reaction, only the leaving group is determinate of the rate of reaction - this may be due to steric hinderance or a weak reagent that can not affect the rate of reaction. In your general Sn2 reaction, the compound that undergoes subsitution tends to have less steric hinderance, and/or you are using a stronger reagent. Thus, the reagent itself also plays a role in determining the rate of reaction since the intermediate stage includes the reagent attacking the compound, forcing the leaving group to leave.
The same concept holds true of the E1 and E2 reaction, except you are eliminating a substituent and not substituting one.
Is that clear?