1. I am on my own today.

2. I am loney today.
3. I am alone today.
4. I am lone today.
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Are they the same in meaning and grammatical?

No, they do not all mean the same. "on my own" and "alone" could mean the same, if one is without company in some endeavor. "I am lone today" is not grammatical at all. And I assume #2 should be "lonely," not loney. Lonely means one longs for company but isn't finding it. "on my own" and "alone" are not necessarily bad things, "lonely" is.

All four sentences are similar in meaning, but there are some differences in grammar and usage:

1. "I am on my own today."
This sentence means that you are by yourself or without any company today. It is a common expression to indicate independence or solitude. This sentence is grammatically correct and widely used.

2. "I am loney today."
The word "loney" is misspelled. The correct word is "lonely." So, the correct version of this sentence would be: "I am lonely today." This sentence means that you are feeling a sense of sadness or isolation because of a lack of company or companionship. It is grammatically correct and accurately conveys your emotions.

3. "I am alone today."
This sentence has the same meaning as the first two sentences. It means you are without anyone else's presence or company. It is grammatically correct and commonly used.

4. "I am lone today."
Similar to the second sentence, this sentence contains a spelling error. The correct word to use here is "lonely." So, the corrected version would be: "I am lonely today." This sentence has the same meaning as the other sentences and is grammatically correct.

In summary, sentences 1, 3, and the corrected versions of sentences 2 and 4 are all grammatically correct and convey the same meaning of being without companionship or feeling isolated.