Form 1099 is an informational return, also 1099 forms are more single purpose forms. 1099-I = interest 1099-d = dividends
A form k-1 is a type of ownership form, A form k-1 is a form which lists the owners share of the business activities as such it can can contain a higher number of information items. A k1 does not represent ownership like a stock certificate but it does report the owners share of the business entities activity.
A form k-1 is issued by Flow Through entities, these are entities that normally do not pay taxes at the entity level but pass income/loss down to the owner or beneficiary. K-1's come from partnerships, S-corporations, Estates, Trusts.
Form 1099 also reports payments, K-1 reports all activities.
I hope this answers your question, if not, please provide additional information or clarifying question. otherwise please click the accept button and Thank You.