Stenosis= narrowing of the normal size of an opening. Stenosis of the spinal canal is a narrowing of the size of the spinal canal that results in compression of the structures in the canal (either nerve roots or spinal cord, depending on the location along the spine- in your case, it would be nerve roots). The foramen is the opening by which the nerve roots exit the spinal canal. Foraminal stenosis results in nerve root impingement, but outside the spinal canal. The symptoms of either form of stenosis would be the same in the lumbar spine- ie, either could cause sciatica. If the compression is at the level of the spinal canal, other nerve roots that run through that area of the spinal canal can be affected. In the lumbar spine, the other nerve roots of concern are the sacral nerve roots that control urinary/fecal continence (too much information?!).
An MRI can readily diagnosis spinal vs foraminal stenosis. Some/many patients (dogs anyway) have both. The compression is typically due to a combination of soft tissues (disc herniation, ligamentous hypertrophy/thickening) and the development or arthritic bone spurs (osteophytes).
An "-ectomy" is a surgery that removes something. An "-otomy" is a surgery that enters or opens something. The lamina is the roof of the spinal canal. Therefore a laminectomy is a surgery in which the roof of the spinal canal is removed (for the purpose of decompressing the cord or nerve roots). A discectomy is a surgery to remove a (typically) herniated disc. A foramenotomy is a surgery that enlarges the size of the intervertebral foramen in order to create more space for the nerve root as it exits the spinal canal.
If you were my patient, you'd be a dog of course, and for your first episode of pain with no loss of neurologic function, you'd be prescribed rest and pain meds. You'd only get an MRI if that approach failed (or, lol, you were a Guide Dog- then you'd get an MRI right away and at a discount to boot).
Hopefully you are feeling better soon.