Can I use my ticket for a different train than I originally planed to?

Within the time frame for which a ticket is valid a person with that ticket can take any train that belongs to the same railroad company and travels through the same route. For example if you originally intended to take a train departing at 12:30 and you have a ticket valid for 6 hours than you can take any train departing after the 12:30 on the condition that you will reach your destination before 18:30.
The sole exception from that rule are the tickets for the trains belonging to the PKP Intercity Company. Such tickets are linked to specific places in specific trains. So they won’t be valid for any different trains.