Checked back in to see what the discussion was producing here and I was amazed at what has happened
First, anything that is threaded is a screw, bolt or nut. Wood screws are screws, hex head cap screws (what most people call 'bolts', the things that hold your cylinder heads on) are screws, bolts are bolts but still threaded and therefore screws. To find out the exact definition and see a picture of each beast, please refer to Machinery's Handbook. Most people who are not machinists or toolmakers will pass out or puke looking at all the data and definitions of each. In my 24th edition Machinery's this data comprises 196 pages, complete with footnotes referring back to various standards set by ANSI. You gotta look that up on your own.
Second, if it is a screw it is available in US/English/SAE - whatever you want to call it as well as metric. So yes Virginia, there are metric lag screws.
Related to all of these screws is a chapter specifically dedicated to various screw threads and threading: unified screw threads, metric screw threads, acme crew threads, square threads, spark plug threads, hose coupling threads, electric lamp threads, and the like. This is another 266 pages....so there are coarse, fine, and extra fine threads. The neat thing about all of this is that there are plenty of mind contorting fractions and decimals in here, which makes it extremely fun reading
In the end, it does not matter if it is SAE or metric, a screw of comparable size in either system that is made out of the same grade of steel will have equal holding power when torqued properly - end of argument over metric being better than SAE or vice versa - it just doesn't matter from the engineering end of holding something together
The only benefit of metric over standard as far as I can tell is for someone who is way way way over the top OCD worse than myself is that with metric you have nice whole numbers forged into your wrenches or sockets which looks a lot neater than those messy fractions - that is unless you need a 4.5 or 5.5 mm socket or wrench. The problem with SAE is that the fractions are not nice and neat thanks to some no grease under the fingernails, pale, i can't lift a 16 oz (0.4536 kg) hammer mathematician said that fractions need to be simplified. Personally I have no problem calling a 1/4" wrench a 4/16" wrench, but would actually prefer 8/32" as I still have some of the old x/32" wrenches and sockets, so it would just make my box look so much neater and uniform
I think we have deviated from the question which is kind of a basic beginner wrench turning question as far as what to have in your box for that first job type of thing. It all depends on what you work on. Newer and/or import cars you can probably get away with all metric, but may need to have one or two SAE wrenches or sockets for those oddball jobs. Older vehicles, trucks, farm implements, and industrial applications will require both. To be a first class mechanic, restoration expert, or customizer will require both plus a heck of a lot more.....I don't think Jay Leno is going to hire you if you show up with more than a basic set of Harbor Freight metric sockets and combination wrenches. For DIY and hobby use you will probably need both. A craftsman is capable of working in or with either system without any undue distress and is capable of using all methods of measurement, including fractions - at least that was what was taught to me in shop in school and when I got into my trade. If you could not read a tape measure or scale ('rule') there was no point in walking through the door.
Just my $0.02 on this (again)