In theory, a lateral merger is the only true merger. The firms are generally of similar size, and the result is a pooling of resources and a balanced recognition of partners from both firms. Who gets which position, whose name goes first, and who has the final say, all must be negotiated in advance. A downstream merger is basically the view from the other side of an upstream merger. A downstream merger occurs when a larger firm seeks out and acquires a smaller practice.
Any firm can actively seek to initiate a downstream, lateral, or upstream merger.
The critical issue is whether all the principals have thoroughly and carefully considered all aspects of each option. Each type of merger has advantages and drawbacks. The key to achieving a successful result is the time and effort spent prior to making contact with the other firm. Knowing what you want and proper planning are critical to avoiding a potential disaster. I recommend using an outside consultant or facilitator to help assure that the discussions are productive, balanced, and complete.