For what you describe, you will need a Turkish Visa because with two separate Itineraries and Tickets, it's not a connecting flight and you are not a Transit passenger.
You have a flight from Manila to Istanbul. Then you have a flight from Istanbul to Romania. So, on arrival at IST, you will have to clear Turkish Immigration, collect your luggage, clear Customs, then check in and check your bags with the next airline.
Even if you don't check bags, you likely will still have a problem since Philippine Airline will only see you going to IST and should insist on you having a valid Turkish Visa, otherwise, they are technically transporting an inadmissible person.
This is how it works pretty much everywhere, not just IST. Travelers from certain countries, France for example, can do this since French Passport holders can travel to Turkey visa-free. Philippine Passport holders cannot.
There is one possible scenario where this will work:
- Philippine Airlines has an Interline Agreement with your onward carrier that includes baggage.
- Philippine Airlines will accept proof of onward travel in lieu of a Turkish Visa because of point #1 and can link your records.
- Turkey's pre-flight electronic manifest screening allows Philippine Airlines to board you without Visa information because of point #1 and point #2.