The I-864A is an affidavit swearing that you would provide support for the incoming alien. This would obligate you to support that person, which is likely why you do not want to sign the Affidavit. If they obtain any government benefits then you could be obligated to reimburse those benefits.
A letter of support is merely agreeing to help provide for the immigrant, it does not carry the weight of the Affidavit and is not a promise to reimburse the government for any assistance. The letter discusses how you may provide a place to live or some assistance for support, but it is not a sworn promise and would not be binding which is why Immigration does not consider them as they would the Affidavit.
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