My experience with reasons for limping:
Foot rot - Crevice of the foot between the "toes" appears to be "cracked open". Smells. Usually gets the blame for the limping. Easily cured with antibiotic. If one treatment does not solve it or show major improvement in a day, suspect something else.
Sprain or injury to leg - ligament/tissue/joint physical injury to any part of the leg structure. Needs confinement/rest. May not recover. Treat for inflammation/pain. People tend to overlook this as a cause since a "shot" won't fix it. Could be a bruise to the soft tissue on the back of the foot as well.
Abscess - infection pocket in the foot due to puncture wound. Can be caused by a nail, wire, sharp stick or metal or similar. Need to be sure that the foreign object is no longer in the foot. Clean the hoof and scrape the bottom of the hoof with a knife blade looking for a hole. Usually will appear as a black/dark spot in the hoof. Hoof needs to be clean to spot it. Use a hoof knife to "dig" out the hole until you start to see some pink/red. Dig just a little more until it drains freely. May be deeper and you may give up too soon. But, don't go too deep. If you lose the black/dark trail, stop. Wrap the foot to "try" to keep it clean. Keep confined if possible. May help to soak the foot in a bucket of water with Epsom salt. Can put a wooden block on the good hoof to keep the affected hoof off the ground. Difficult to treat with antibiotic only due to getting the antibiotic to the abscess. Antibiotic only treatment will usually follow a pattern of getting better and then limping returns when the antibiotic wears off. Foot will be swollen. If untreated, the abscess will eventually "break out" the side of foot just above the hoof and self drain. May have permanent joint damage if left untreated. Be careful with the hoof knife - holding the hoof with one hand and cutting with the other. Hoof knife can slip and cut your hand. You will meet some nice people in the emergency room that will be fascinated with what you were doing.
Something stuck in the foot - rock between the hooves, roofing nail in hoof, etc. First thing to look for. Lift the foot and inspect. Scrape the bottom of the hoof with a knife blade - dull knife preferred which I usually have.
Hairy heel wart - never had it, but looks real nasty. Looks like raw meat. More common in dairy than beef. Spreads to other animals from walking on contaminated surfaces.
First step in diagnosis is to get the animal confined and clean and inspect the hoof. Second step is treatment. Tendency is to just give an antibiotic and skip first step.