Helping people with computers... one answer at a time.
This one's tough because there are so many variables that aren't specified. But the bottom line is that it's all about the email program you're using. And I'll bet that they're different programs at work and home.
If you're home email program isn't the same as the one at work, it's quite possible that's the root of the problem. Some programs don't automatically show attached pictures in, or below, the message body when you look at a message. Outlook Express, for example, does. Outlook does not, and there's no setting to make it do so.
Another option is that perhaps your email program at home is "protecting" you from embedded pictures. Check your security settings - Outlook, Outlook Express, Thunderbird & others now don't show pictures by default - you might simply need to disable that or perhaps add the sender to a "safe senders" list.
If you forwarded the mail from one account to another (say from work to home), it's possible that the mail client at work took the images embedded in the message and changed them to be attachments. It's possible that the sending mail client either just does it that way, OR you received the mail as HTML or Rich Text, and forwarded as plaintext. The later can't show pictures, hence would have to convert to attachments.