Is the heart a tissue or an organ?

Yes

The heart is a muscle tissue - cardiac to be precise

Any living piece of an organism is a tissue

Tissue is a cellular organizational level intermediate between cells and a complete organism. A tissue is an ensemble of similar cells and from the same origin, that together carry out a specific function.

There are four main types of tissue:

connective

muscle

nervous

epithelial

There are three types of muscle:

smooth

skeletal

cardiac