Hi @cp1132 ,
Thanks for reaching out!
I understand that you would like to have a search bar similar to the one displayed at the above-mentioned site, is this correct?
This is highly dependent on the theme a site is using, rather than WooCommerce core itself and it may be helpful exploring themes that have this exact, or similar, search box style.
I have checked the WooCommerce.com Marketplace and found a theme that has a similar search style to the one you are after.
If you are using the Storefront theme, the Storefront Powerpack extension allows you to customize almost every aspect of theme without any code!
WooCommerce.com offers a 30-day refund policy which you can take advantage of, allowing you to test an extension and/or theme, and make sure that it is what you are looking for.
If you prefer to maintain your current theme (or if you are not using the Storefront theme), changing this would require either overriding the product search box, or using a plugin with a purpose for doing this.
You can read more about Overriding the Product Search Box here.
Alternatively, you can search the www.remarpro.com plugin repository for a plugin that may help you achieve this.
On the other hand, if I misinterpret your concern in any way, please provide additional information on what you are trying to achieve.
Cheers!