What's the difference between "woulda" and "would've"?
Solution 1:
First, the question has the same answer with most other modal auxiliary verbs besides would, e.g:
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would have, may have, might have, must have, should have, could have
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would've, may've, might've, must've, should've, could've
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woulda, maya, mighta, musta, shoulda, coulda
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/wʊdə, meyə, maytə, məstə, ʃʊdə, kʊdə/
Willa is unusual, because will have is unusual; normally will prefers to contract with a subject (ideally a personal pronoun) rather than with a following have. And shall, the remaining modal auxiliary, never appears with a following have in American English, since it's restricted to two first person question constructions exemplified by Shall I open the door? and Shall we dance?
Phonologically, the auxiliary have in these compounds is never pronounced /hæv/ like the verb halve; since the modal is stressed, the have is unstressed, and therefore reduced to a central schwa vowel /ə/, like what happens to the to of want to, got to, have to resulting in wanna, gotta, hafta in eye spelling, or /wanə, gatə, hæftə/ in speech.
All that's left of have, in unstressed position, is /əv/, and that's why people spell these constructions might of and should of, etc. It's the best way English offers to represent what people say, and people take any opportunity to be clear when they can.
The question of whether the /v/ of /əv/ gets pronounced or not usually depends on (a) how fast the speaker is talking and (b) what sound comes after the /v/. But there are other factors as well, and one speaker will vary a lot from one instance to another, and speakers will vary from one another individually, so it's not a matter of just two representations. To say there are no hard-and-fast rules is to understate the case; it's moment-to-moment individual judgement all the way.
Generally, it's hard to say /v/ before another consonant; names like Vbirski or Dromovd look difficult to pronounce, whereas Varski and Dromova don't. But it's possible, and some people have convinced themselves that they always say might've with a real /v/, no matter what they actually do. Some even believe they're really pronouncing have, again no matter what.
This is all about the language. English spelling is just medieval technology, so it's no wonder eye dialects of all sorts spring up everywhere.