symapi.log files contain interaction between symcli commands and the code running in the storage. If a command fails due to a syntax error or due to failed local test (within S.E.), symapi.log won't contain details. Thus don't expect to find ALL commands in symapi logs.
Of course you can increase verbosity but usually you'll find all messages/questions/answers/commands between S.E. and the box.

storapid.log describes activity of storapid daemon. Since S.E. 6.x you have a set of daemons that manages interaction between S.E. and the box. storapid is simply one of the daemons. Try running "stordaemon list" to have a list (and corresponding status) of all available daemons.

S.E. have a number of variables/options to fine-tune log behaviour. The default behaviour for daemons is to simply overwrite older logs. The default behaviour of symapi is to switch logfiles every day keeping all past files. You can obviously change these defaults if you have space on your drives