There are hundreds of ways of joining tubing to make bike frames.
Most manufactures are looking for cheaper and faster and simpler.
ElectroForging was Schwinn's mass production method used to make 100,000,000 Chicago built bikes. Flash welding is slapping 2 electrified parts together. It was a ballet of motion and timing, turning off the power at just the right moment where the 2 parts were held in moveable jigs. Followed up with the "finish on top" to remove the excess flashed steel. Varsity, Continental, Breeze, Racer, Stingrays, Krates, Cruisers, Twinns, Pixies, etc. Started in the 1950s, designed to look like brass fillet brazing but far faster. Schwinn was cranking out some 10,000 bikes per day at their peak using this method. Schwinn EF died in 1983 when they closed the Chicago factory and sent some of the EF equipment to Murray to mess around with for another couple of years. I've had a few Murray built EF Schwinns and they were a disaster. Schwinn continued to make bikes using brass fillet brazing and brazed lugs for their more expensive bikes.
"Welding" is a specific manufacturing process that means melting the two base metals and letting the liquid metals flow together. Feeding in extra metal of the correct alloy is optional. Then letting them freeze (it's a relative term) back in to a solid. Welded metals need to be thicker to withstand the abuse of welding. Internal stresses are super high as a result of the rapid cooling. Some metal frames need to be annealed to relieve the stresses. Generally welding has bad side effects for strength and durability. Cracks are a result of stress and fatigue. Especially bad news for bridges. BTW the oldest metal bridges were iron and hot riveted together. They will out last any newer welded steel bridges and any concrete bridge.
Many use "welding" in a very broad sense, many so called welding methods aren't actually welding. Brass Brazing is not welding. You can weld using an oxy torch by melting the steel and adding a filler.
Mig & Tig are relatively new welding methods used on bike frames starting in the 1990s. Mig is especially good for robotic welding of cheap bikes. There are newer steel alloys designed and manufactured to be tig or mig welded. Reynolds 853 for example. Reynolds 531 was designed for brass brazing where the temps are kept low enough to melt the brass alloy mix but not affect the steel itself.
Screwed & Glued. Lots of bike frames have been made using thermal set glues. The big advantage is you never heat the metals above the glue setting temperature (~240f) so the metal is never affected. Manufactures can use much lighter tubing because it retains its full manufactured strength. Vitus, Meridia, Trek & Raleigh are some of the big companys that used various glue methods. The early bonded Trek frames uses square cut tubes (no miters) put into cast head tubes, bb shells, seat lugs, drop outs, etc. No need to have highly trained factory workers and it took less time and the bikes were lighther weight.
I'll mention the early aluminum frames by Caminargent (1930s) and Monark (1940s). Tech taken from the German air ships that were made of "duraluminum". Bolted together long before aluminum welding was invented.
Welded aluminum frames. First popularized by Gary Klein, later dominated by Cannondale and now the Asian builders. Once welded, aluminum need to be heat treated. Frames need to be put in sturdy jigs to hold their shapes before going in the ovens. The early canonadales were made using very thick walled aluminum. With modern hydroforming, the aluminum is almost too light. Frame failures are very common in race bikes.
Most bikes were brazed from the 1870s to about 1960. Hard to call them mass produced as brazing is a time consuming process. The 1960s really saw the start of crap bikes by the USA builders. bb shells were flat steel rolled in to tube shape,holes punched out for the tubes that were tack brazes. Rear dropouts were thin mild steel spot welded to crushed flat stays. Stays and tubes were all gas pipe. Of all the largest quantity bike building companies in the USA, only Columbia is still in business and they only make office furniture, a more suitable product for these cheap manufacturing methods. Huffy, Schwinn, Roadmaster, etc are all just marketing names for big box products from Asia.
Brass brazing is now left to the artisan builders. The pre-ef Schwinns and the brass fillet Schwinns are surely heavier due to all that extra brass. But it has the nice curves that support the tubes very well. You rarely see failures in fillet frames. Using lugs at the joints means far less brass (or silver) and lighter tubes. One big problem with brass brazed lugged frames is over heating that affects the steel. It's all too common to see frame failures near the lugs or down tube shift lever braze ons.
There are bikes that are a mix of lugs and fillet brazing. Usually where the manufacture couldn't source the exact shape of lugs they wanted. Tandems are a common example.
Combo frames. Plenty of bike frames have been built using nearly every combination of materials. Raleigh's Technium line of bikes were glued (bonded) aluminum front triangles with brazed steel rear triangles. You can't weld steel to aluminum but you can glue them together. Many high end race bikes were carbon & aluminum or titanium bonded to carbon and so on. Treks earlier "3 tube carbon" frames were carbon fibre wrapped over very thin aluminum tubes then glued into the lugs. Very light and stiff.
Carbon fibre bike frames are never welded.
Kabuki had a "cast in place" aluminum & steel frame. The steel tubes were inserted in to molds and molten aluminum was poured in to the molds. The molds had fake spear points for decoration. One model used polished stainless steel tubes to make it more suitable for salty climates near oceans.
There were a couple of attempts of plastic injected molded bike frames.
Wood & bamboo. A couple of makers use bamboo for tubes, joined with hand wrapped carbon fiber and epoxy.
Wood can be anything as most are individually custom built. One engineering school contest was to build a rideable bicycle solely from a 4x8 sheet of plywood and nothing else other than glue. There are some wood bikes that are true works of art. Laminate is another method.
When I took welding classes I learned about plastic welding. Many travel mugs are actually welded by spinning the inner and outer shells until the contact areas melt, stop the spin and they cool as 1.
Now I have a plastic welder that pushes hot wires into plastic. Very handy for fixing car bumpers. Sure beats a roll of duct tape.
Some methods use electric induction as the heat source. I'll stop here.
