How many records can a MySQL MyISAM table store? How many InnoDB can?
You can't count by number of records because your table can have really short records with only a few int fields or your records might be really long with hundreds of fields.
So it has to be measured in the file size of the tables.
For MYSQL: The table size limit is based on the operating system drive file system that MySQL is installed on, ranging from 2GB to 2TB.
See the MySQL reference manual for full explanations of limits for each operating system.
Concerning InnoDb and MyIsam i do not know.