This paper presents TabSketchFM, a neural network-based table model, to address the growing enterprise need to identify related tables (tables that are unionable, joinable, or subsets of each other) in their data lakes. TabSketchFM improves the data discovery efficiency of neural table models through a sketch-based pretraining method and fine-tunes the pretrained model to identify unionable, joinable, and subset table pairs. It demonstrates significant performance improvements over existing neural table models and highlights sketches that are crucial for each task through detailed ablation studies. Furthermore, the fine-tuned model is used to perform table search (the task of finding other tables in the data pool that are unionable, joinable, or subsets of a query table), demonstrating significant improvement in F1 scores compared to state-of-the-art techniques. Finally, we demonstrate the model's generalizability by demonstrating significant transfer learning performance across diverse datasets and tasks.