It depends.
It depends on the client -- some clients allow concurrent access; some will serialize access, thereby losing the expected gain. You have not even specified PHP vs Java vs ... or Apache vs ... or Windows vs ... Many combinations simply do not provide any parallelism.
If different tables, there is only general contention for I/O, CPU, Mutexes on the buffer_pool, etc. A reasonable amount of parallelism is possible.
If same table, it depends on the indexes and access patterns. In some cases the threads will block each other. In some cases it will even "deadlock" and rollback one of the transactions. Deadlocks not only slow you down, but make you retry the inserts.
If you looking for high speed ingestion of a lot of rows, see my blog. It lays out techniques, and points out sever of the ramifications, such as replication, Engine choice, multi-threading.
Multiple threads inserting into the same tables -- It depend a lot on the values you are providing for any PRIMARY
or UNIQUE
keys. It depends on whether other actions are taken in the same transaction. It depends on how much I/O is involved. It depends on whether you are doing single-row inserts, or batching. It depends on ... (Sorry to be vague, but your question is not very specific.)
If you would like to present specifics on two or three designs, we can discuss the specifics.