Hi,
Well, there is a products export / import functions.
On the products listing in your backend, you have the "export" button to get a CSV of the data of your products.
And in the menu Products>Import you can import CSV files with the data of the products.
However, these have some limitations.
For example, if you have created custom product fields on your website, you'll have to create them first on your new website so that the data of the products can be imported in them.
Same for characteristics, you need to created them and their values first in the new website.
Also, the CSV file doesn't contain the images and files of the products. You'll have to manually copy them from the images/com_hikashop/upload/ and media/com_hikashop/upload/safe folders (or other folders if you changed the path in the HikaShop configuration's Files section) via FTP.
Also, the import can create the categories for you, but the export/import don't support all the categories data, only the basics.
A more complete solution would be to export / import the tables hikashop_product, hikashop_price, hikashop_related, hikashop_product_category, hikashop_category, hikashop_variant and hikashop_characteristic from your old PHPMyAdmin to your new PHPMyAdmin. You would still have to move the images and files via FTP, though, but it can be an easier method (for example, if you have hundreds of characteristics, this method is better since you don't have to manually create the characteristics and their values via the interface). Now, using this method, you need to be careful if the table prefix is not the same between both joomla websites as you'll have to modify it.