Is there a specific word for this kind of re-sealable plastic seal?

The US Transportation Security Administration (TSA) officially refers to it as a zip-top bag. I have never heard or read this usage elsewhere, and I imagine it was probably constructed to avoid the genericized trademark Ziploc.

In the southeastern US, a resealable plastic bag is usually called a ziplock bag, regardless of whether it has a zipper or not. This is likely true for elsewhere around the US but I can't vouch for that.

Oddly enough, this Web site features macro-images of the bags and several identifying buzzwords, including slider seal, closures, channel, and double zipper seal.

These are usually called "Press Seal" or "Press-Seal" or "Press-N-Seal" or "Press 'n' Seal" bags. Google "press seal" and look at all the references.

Resealable seems to be the British English word and the words Robusto said are American English. Supermarkets say resealable (if anything), such as Tesco's bags.

i just had a search on ebay for zip lock bags and it seems the UK equivalent and proper nomenclature is 'GRIP SEAL BAGS' for the exact type of seal you're talking about.