> Is a fertilised egg a different type of egg to the unfertilised egg?

No. Same with worker eggs. Only the one type of egg. 

Two types of results from fertilized eggs, though. It has to be heterozygous for the sex allele to develop into a female. Rarely, homozygous diploid drones occur, usually as a consequence of inbreeding. Also, in the Cape Bee, there is the special case of worker eggs producing females but that is a long story and not particularly relevant to the issue. 

> The Cape honey bee is unique among honey bee subspecies because workers can lay diploid, female eggs, by means of thelytoky

there is a good diagram of the chromosomal basis of this at 

https://en.wikipedia.org/wiki/Cape_honey_bee

PLB

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