"Bribery is basically where somebody is in the Bahamas with the money. We're talking about a development programme for Welsh schoolchildren," he told BBC radio.
"They are a million miles apart in my view, otherwise of course I wouldn't be adopting the position that I am in relation to it," the Southampton director said.
Kelly quit after a meeting of the F.A.'s executive committee investigating a 3.2 million pounds ($5.39 million) unauthorised grant or loan to the Football Association of Wales.
The deal was in exchange for Welsh support in backing Wiseman's bid to become a FIFA vice-president.
The committee also passed a unanimous vote of no-confidence in Wiseman but the 52-year-old refused to quit.
Wiseman insisted on Friday that he saw no reason to quit and explained the background to the affair.
"The FA were requested to consider the possibility of offering some help for their (the Welsh FA's) development programme and they were also wishing to stand at that time for the FIFA position that we were hoping to obtain," he said.
"They indicated to us that their development programme was of more significance to them than the particular job in question and that they would be prepared to ask their council to support England for that if we were able to consider offering them some help in their development programme."
He said the English FA would "welcome support from anyone in that situation."
Wiseman said that he believed the FA executive committee had acted wrongly on Tuesday.
"The constitutional position is that the council of the Football Association elected me and only the council of the Football Association effectively can take that position away," he said.
"I am simply exercising what I think is a perfectly proper and sensible right to have the matter taken back to the council.
"I think the process adopted so far is effectively unconstitutional and I simply want the opportunity to speak to my own council. What follows to that we shall see."
Wiseman said that Kelly, as a senior paid employee of the association, had been under different pressures and had decided to quit for his own reasons.
"He had to take his own personal and financial and practical circumstances into account. In a free situation I don't think for one moment he would have wanted to resign," he said.
Reuters
