"I've heard a throw off referred to as a strainer? Why?
Ahem.....from one who has spent way too much time studying and being baffled by the antiquities of membranophones.....In my opinion, a strainer and a throw off are two different terms describing two different things that were invented at different times, but are both commonly used to describe the throw off mechanism.
This is the simple non linear chronology, and this is by no means authoritative; On many early military drums several centuries back and them some, the ends of the cat gut snare strings were simply placed between the hoop and head on each side and pulled tight by hand before tightening up the heads with the rope tensioners. This did not involve a strainer or throw off. One would set it and forget it and hope it didn't rain. To adjust the snares again the ropes would have to be loosened and the snares reset.
Then came what I call the strainer butt, a piece of leather, wood or metal that had many holes punched through it. One very long or several shorter strings of gut were threaded through this on one or both sides. Again, the strings were pulled tight by hand and placed between the head and the wood hoop . In the second picture you can see that this would have made it easier to get the snare strings set.
The next development was probably the early metal screw mechanisms which consisted of a bar clamp or a hook which would hold the snares in place. Attached to this was a simple thumb screw going through a bracket on the drum which one would turn to cinch up the snares. There was no lever. One either tightened or loosened the thumb screw to adjust tension of the snares. The strainer butt would be on the opposite side of the drum. At this point the metal mechanism may have been referred to as a strainer as well.
Why was it called a strainer? One definition of a strainer is a device that stretches or tightens something. It also may have been because the holes in the leather butt piece may have resembled the holes in a cooking strainer or collandar. The catgut snares definitely resembled spaghetti.
Strainers were invented before small concert snare drums and drum set snare drums came into common use. They were used primarily on military snare drums and a quick release lever was just not necessary. It would have been a waste of metal that could be used for bullets. Though there were a few early throws that were invented during the Civil War era but they didn't become prevalent until later.
Most likely the throw off lever became prevalent around the time that drums started being used in theaters during and after the civil war, allowing the drummer to get two sounds from his drum; the regular snare sound and the snare-less effect sound of the Native American or Chinese tom tom. A simple lever with a handle would be used to "throw off" the "strainer" quickly instead of the laborious thumb screw, though the screw remained for tension adjustments. Snare drums were starting to be made smaller and smaller for the convenience of transporting them by the theater drummers, and so they would fit in the tight spaces of the orchestra pit. The drum set evolved out of the theatre drummers' and juke joint drummers' need to play multiple instruments at once. The throw off lever gave the drummer two drums in one. The next gizmo to follow was the bass drum pedal. DOH! Fire the bass drummer!
The coiled snare wires were invented around the turn of the twentieth century, replacing the cat gut snares eventually. The gut snares were very prone to stretching with the weather and humidity. The early Ludwig metal throw offs had multiple holes at the very bottom of the metal strainer unit to thread gut snares through. Of course coiled wires were soldered to end plates then attached to the throw off with strings needing only two of those holes, so that type of throw off could accommodate both gut and coiled wire snares.
So, modern day drums have a throw off, which is comprised of the strainer and the throw lever within the same mechanical piece. The strainer is usually the tensioning mechanism that the snare wires are attached to that you adjust usually with a thumb screw, and the throw off is the on/off lever attached to the strainer to release the snares for the tenor drum effect. "Throw" is the abbreviation of throw off. Of course there are many variations on the mechanism and new versions come out all the time. I personally think that the simplest ones are better just because there is less to go wrong. One of my favorite simple throw offs is the Noble and Cooley brass throw off.
Snare wires is the proper full term for the snare unit though the abbreviation "snares" is used as well. And, yes, snare drum is the other meaning of the abbreviation "snare".