If you have a home office and that is your only office, they are business miles. Otherwise they are commuting.
I am a contract pilot. Can I deduct equipment purchases ( headset-sunglasses , navigation charts ,etc ) deduct?
If you are a W-2 employee then NO.
If you are a 1099 contractor then maybe ... these must be considered ORDINARY & NECESSARY expenses for your line of work and reported on the Sch C.
If you file a schedule C as an independent contractor, you can deduct ordinary unnecessary business expenses. However, when the expense is also potentially of a personal nature, you would have to prove, if audited, that the item was use 100% for business, or you would have to have a reasonably reliable method of determining the percentage of business use and only deducting that percentage of the cost.
I would imagine that charts and a headset would only be used for your professional flying, although if you also used them for your own personal pleasure flying, then you would have to keep records of the number of flight hours or some other method of determining the percentage of business use. Something like sunglasses or a tablet computer used as an electronic flight bag might be harder to prove it was used 100% for business.