The Brother 651 and 661 sewing machines differ primarily in their features and capabilities. The Brother 661 typically offers more built-in stitch patterns and advanced functions, making it suitable for a wider range of sewing projects. Additionally, the 661 may include features such as an automatic needle threader and a larger workspace, enhancing usability for more complex tasks. In contrast, the 651 is more basic, catering to simpler sewing needs.