TRACON Controller described an airspace incursion event when misreading the data block symbology. The reporter noted that the subject symbols should be changed to prevent future errors.

Narrative

A PA31 departed IFR to the northeast; climbing to 5;000 FT. When the PA31 was approximately 10 miles from the second boundary; I gave him a frequency change to contact them. I thought that I had flashed him and they had taken the hand off. One ARTS symbol is N and the other's hand off symbol was an H. I thought the N was an H and I switched the aircraft. During that time a large line of heavy rain was moving west to east over the first (N) airport; with arrivals coming inbound to land. Although the traffic level was low; the complexity was starting to build with arrivals not wanting to land at the main airport; wanting to divert or hold. I then noticed when the aircraft was 10 miles into the second airport's airspace that he was not on the correct controlling symbol. I immediately called the second airport's Tower (H) and made sure they had RADAR contact and did an automated hand off. I recommend that the controlling symbols be changed; so they don't look similar. [Also]; slow my scanning down. If I had slowed down; I may have noticed that the aircraft was not properly handed off.