I am preparing for Pearson Test of English (PTE) Academics for further study.I score less in spelling and I know that this forum is for English Language not for any 'test regarding English language proficiency'.
so I want to ask question in the context of rules of English Langauge that 'she drew in a quick breathe' here breathe is incorrect as breath must used. So breathe is spelling mistake or grammar mistake ?
Similarly, if I write 'He licked the car' instead of 'He liked the car' So licked is spelling mistake or grammar mistake?
The two mistakes you described seem to both be spelling mistakes rather than grammatical mistakes.
Spelling mistakes happen when you wrongly transcribe a word.
For example, if I was not familiar with your name, I could misspell it as "Amon". This mistake has nothing to do with my understanding of syntax or grammar.
Grammatical mistakes usually happen when you utilise a word form that is not compatible with the context in which it is used.
For example, if I wrote "We likes ice-cream" that would be a grammatical mistake rather than a spelling mistake because "likes" is not the correct form of the verb.
A shortcut to figuring out if something is a grammatical or spelling mistake is to consider if a sentence would be "correct" in an oral context (rather than a written one)*. If you create a sentence and it's incorrect when written, but correct when pronounced, then it could give you a hint that your mistake is probably one of spelling and not grammar.
* Of course there are exceptions to that: there are grammatical mistakes, such as punctuation mistakes, that can only exist in written language. I probably made a couple above :)