There are certainly things that closed shops and single union agreements have in common. However, they are different things. They are different enough that, in the UK, closed shops are illegal but single union agreements are common.
A closed shop is a company or a workplace in which membership in a particular union is compulsory. Anyone who wishes to work in that particular firm or workplace must belong to that union. This precludes the possibility of any other unions representing workers and it also precludes the existence of any workers who simply do not belong to any union at all.
By contrast, a worker in a workplace with a single union agreement need not necessarily belong to a union. Under such an agreement, only one union is recognized by the employer. The employer will not bargain with any other union. However, the workers are not legally required to belong to that union. They may belong to any union they wish or to no union, but only the one union that has made the agreement will be allowed to bargain for them.