mihai-rotaru

Simple plugin which wraps a Twitter widget as a WordPress widget.
In order to use it, you need the Twitter widget’s ID – something like 
332108549298064896. You can see it in the embeddable code Twitter gives you 
after you create the widget. You also need the Twitter username for the account 
the widget belongs to.

Proper Twitter Widget

Makes available a widget which contains a Twitter feed.

oniswap

Important notice: Twitter shut down their v1 API and use now the v1.1, to update your mini twitter feed you need to go on https://twitter.com/settings/widgets/new create a new widget and get your Twitter widget ID. You can update the id on the shortcode or widget. ([minitwitter id=”TWITTER_WIDGET_ID” username=”YOUR_USERNAME”] or in the field “id” in the widget section). 
You get this Twitter Widget ID from the code provided by Twitter when you create this widget: data-widget-id=”TWITTER_WIDGET_ID” or in the URL https://twitter.com/settings/widgets/TWITTER_WIDGET_ID/edit.
The plugin “mini Twitter feed” or twitter timeline puts Twitter on your WordPress blog, you can add your tweets or the tweets from the folks you like, lists, queries…
You can display up to 100 tweets within 7 days (limit set by Twitter’s Search API).
It displays tweets from your feed or from the Twitter Search, from a list or from your favorite users. It is very flexible and modular.

Mini twitter feed

Embed your twitter feed or the twitter timeline from your favorite users on your Wordpress blog. Shortcodes and widgets are used.

Proper Twitter Widget vs Mini twitter feed