Are Segments, Packets and Frames the same size if we ignore headers?

Each layer have its header, as you can see:

• Segments: Transport layer (TCP/UDP) = transport header + data (from upper layer)
• Packet: Internet layer (IP) = network header + transport header and data (both transport and data from upper layers)
• Frames: Network layer (Ethernet) = frame header + network , transport header and data (from three upper layers).

So, to answer your question, the difference between segment, packet and frames are basically what its respective layer consider as "data". On a segment, data comes from the application layer; on a packet, data comes from the transport layer (transport header + data); and on a frame, the data comes from the internet layer (transport and internet headers + data from application layer).