Well it all depends on what the CSS is doing.
strong {
font-weight:bold;
}
will make it appear bold. Some browsers will have that set as a default CSS rule, others might not. Have you set anything that says explicitly that strong or <b>
will result in bold text?
Generally you shouldn't rely on the browsers to style elements on their own. For example, Safari might say:
strong {
font-weight:bold;
font-size: 1.2em;
}
while Firefox may have:
strong {
font-weight:bold;
color: #000000;
font-size: 18px;
}
or something like that. So when different users view your page, it may or may not look the same.
Investigate reset.css files (maybe here) and think about telling the browser WHAT you want it to look like via CSS.