Oncogene amplification is a major driver of cancer pathogenesis. Breakage fusion bridge (BFB) cycles, like extrachromosomal DNA (ecDNA), can lead to high copy numbers of oncogenes, but their impact on intratumoral heterogeneity, treatment response, and patient survival are not well understood due to difficulty in detecting them by DNA sequencing. We describe a novel algorithm that detects and reconstructs BFB amplifications using optical genome maps (OGMs), called OM2BFB. OM2BFB showed high precision (>93%) and recall (92%) in detecting BFB amplifications in cancer cell lines, PDX models and primary tumors. OM-based comparisons demonstrated that short-read BFB detection using our AmpliconSuite (AS) toolkit also achieved high precision, albeit with reduced sensitivity. We detected 371 BFB events using whole genome sequences from 2,557 primary tumors and cancer lines. BFB amplifications were preferentially found in cervical, head and neck, lung, and esophageal cancers, but rarely in brain cancers. BFB amplified genes show lower variance of gene expression, with fewer options for regulatory rewiring relative to ecDNA amplified genes. BFB positive (BFB (+)) tumors showed reduced heterogeneity of amplicon structures, and delayed onset of resistance, relative to ecDNA(+) tumors. EcDNA and BFB amplifications represent contrasting mechanisms to increase the copy numbers of oncogene with markedly different characteristics that suggest different routes for intervention.