When you "purchase" fonts, you are in reality purchasing a license to use them, in much the same way as we license software. If you have purchased a license for yourself, then your license means you can't just send the font files to your client. If your client needs the font files, then they will need to buy a license, or you can buy another license on their behalf. Just remember, that at checkout, you need to enter your client's name or company name in the Licensee field.
If you are working on a website on behalf of a client then you are usually permitted to purchase the webfont files and use these to create the website for the client. Again, you would put the clients name in the Licensee field.
We say 'usually' permitted as you would have to check the EULA of the specific Foundry Partner in order to be sure. This tells you exactly how their fonts can be used.
Tip: if you use the fonts to create a graphic or a logo, for example, then your client most likely won't need to edit your design, and so won't require a license for the fonts.
For specific and detailed instructions and where and how you can use a font, please read the relevant Foundry Partner's EULA