The use of 'alot' instead of 'a lot', whether written or spoken, causes no inherent difference in meaning (without getting theoretical) other than its violation rules of prescriptive and stylistic grammar. In other words, it is only a violation against standard English. There stands little difference between the two words in most pronunciations except for syllable length or barely pronouncing any vowel before 'lot'. I would not advise any English learner on this site to use the word 'alot' in either writing or speech unless for the purpose of making a point about the standardization of language– i.e., in literary fiction, or unless the learner would like to speak in a more common manner. I am sure that in almost every printed context the word would be labeled unacceptable by a proofreader or copy-editor.