A charter 737 would fall under the Supplemental section of 121. That is the equivalent of 135 ops in aircraft too large to be covered under 135. At one time Part 135 "reverse defined" a DC-3 as the largest aircraft that could be operated under 135. It talked about an aircraft that could carry 7,500 pounds 186 miles with 350 pounds of engine oil.
A company can have two sets of Ops Specs. There can be 135 Ops Specs covering smaller aircraft and 121 Ops Specs covering larger aircraft. The aircraft are listed on the Ops Specs and would not move between them. Pilots could fly both as long as they had completed both training programs. It becomes interesting trying to keep their flight and duty times straight because the rules are different.